A Brief Overview of Positions Concerning Issues 
Related to the Doctrine of  "The Perseverance of the Saints"

The Christian community is divided largely between three theological viewpoints on the following issues. I use the labels "Free Grace", "Lordship Salvation" and "Arminian" not so much as themselves being descriptions of their individual theologies, but rather simply because those are the terms I find most commonly being used today to describe these divisions.
By the way what today is referred to as Arminian Theology is not actually the theology of it's originator Joseph Arminius on this point. For Arminius writes, "Election to salvation comprehends within its limits not only Faith, but likewise perseverance in Faith." And thus is essentially a Calvinist on this issue.

So also though often characterized as Arminian, Charles Finney advocates the doctrine of the Perseverance of the Saints, saying, "Another effect of gospel justification is to ensure sanctification. It not only insures all the means of sanctification, but the actual accomplishment of the work so that the individual who is truly converted will surely persevere in obedience till he is fitted for heaven and actually saved." That is actually the position of Lordship Salvation.

Anyhow, the question is which of these is most consistent with what the Bible teaches. For myself I believe it to be the "Lordship Salvation" position. I've underlined those places where two theological viewpoints agree.

Free Grace
Lordship Salvation
Salvation By grace through faith same same
Eternal Security Yes Yes No
Assurance of Salvation Absolute regardless of one's behavior Relative to one's behavior Relative to one's behavior
Fear of going to Hell No Fear Fear that one might have never been saved to begin with Fear that one might lose their salvation
The Correlation between one's behavior and one's salvation status Not necessarily any correlation - or perhaps a trivial correlation. It is possible for those born of God to live a lifestyle of sin and even fall away from the faith, but not lose their salvation It is inevitable that those born of God will continue (as in lifestyle or professional sense) in the faith and in a living consistent with that faith to the end. It is possible for those born of God to live a lifestyle of sin or otherwise fall away from the faith and by doing so lose their salvation.
Nominal Christians Don't exist Their faith is not of salvific value.
(Faith is God's condition for salvation, but not any kind of faith. It must have both the right object and right quality to qualify)
(I assume the same as with Lordship Salvation)
However I suspect that some in the Arminian camp would advocate the idea that it's easy to be saved (trivial faith to enter), but hard to maintain one's salvation status. 
Works They are irrelevant to salvation They, along with a continued faith, indicate one's salvation status
(works viewed as an effect)
There are also works involved in the development of saving faith from its nominal stage in cooperation with the Holy Spirit. But such are pre-salvation works.
They, along with a continued faith, determine one's salvation status 
(works viewed as a cause) 
However, to be fair, there those among Arminians who view works purely as an effect of faith, but don't view Perseverance of faith as an inevitable effect of being born of God.

Usually I find what happens if one holds either the Free Grace or Arminian positions is that they won't acknowledge the Lordship Salvation position. But rather those of a Free Grace position will simply reckon the Lordship Salvation position to be an Arminian position, and Arminians will reckon the Lordship Salvation position to be simply a Free Grace position. And the two extremes will tend to demonize one another, whereas peace and unity can be found in this center position, which I believe to be the most Biblical. Both sides have their strengths and weaknesses. Both sides are Christians. Both sides have studied the Bible. But both sides cannot be correct. The weaknesses of each side are resolved in this center position.

Those of an Arminian position will propose that the Free Grace position tends to promote a carefree licentiousness attitude in the Christian community and discourages doing good works, and deceives nominal Christians into thinking that they are saved, not preparing them for the judgement day.  Those of a Free Grace position will propose that the Arminian position tends to promote Legalism in that such a theology can easily lead to one making one's works the object of faith to maintain one's salvation status. I agree with both objections, but these are unlikely the case of Lordship Salvation.

Verses Supporting concepts unique to Lordship Salvation

A Christian is presently saved only if they endure to the end. (Which also logically means that if a person is presently saved, he will endure to the end. For if they don't endure then had never been saved)  This is a position unique to Lordship Salvation. For both Free Grace and the Arminians say that a Christian is presently saved regardless of whether they endure to the end. For both groups hold that a person's future behavior has no bearing on their present condition. Although the Arminians will say that future behavior has a bearing on a person's future condition, but not on his present or past condition.

The main thing which is unique to Lordship Salvation is the idea of being born of God has an inevitable and permanent effect on a person's behavior, preventing the person from living a lifestyle of sin. What does the Bible say?

Consider for example 1John 2:19

"They went out from us, but they did not really belong to us.
For if they had belonged to us, (ONCE SAVED)
they would have remained with us; (ALWAYS SAVED)
but their going showed that none of them belonged to us."
Past Event: "had belonged"
"would have remained" is in the Pluperfect tense which indicates an event viewed as having been once and for all accomplished in past time.

Once a person is born of God not only is their salvation status secure, but also they will inevitably continue to endure in their faith and in a lifestyle consistent with that faith to the end.

1John 3:9,10
"No one who is born of God will continue to sin, because God's seed remains in him; he cannot go on sinning, because he has been born of God. This is how we know who the children of God are and who the children of the devil are: Anyone who does not do what is right is not a child of God; nor is anyone who does not love his brother."
Past event: "because he has been born of God" In the Greek this is in the past perfect tense. What is true of those who in the past have been born of God? They have lost the ability to go on sinning.  John of course is speaking in a lifestyle sense for he already acknowledged that those born of God can sin in the aorist (non-lifestyle) sense. The word "cannot" in "he cannot go on sinning" (vs 9) is the greek word "dunamai", from which we derive the English word "dynamite", and it refers to the person's ability. This is the effect of being born of God. It affects the person's will such that it is inevitable that those born of God will exhibit behavior characteristic of children of God. If a child of God tries to live a lifestyle of sin, they find that they cannot do it, just as those who have not been born of God find they are incapable of living the Christian life. As such they are incapable of falling away, and thus he speaks of them not continuing to sin, but rather continuing to remain.  These are descriptions rather than conditions, for there are no "if's" found here.

So we see that we can measure whether one has been born of God based on their behavior. But if one falls away from the faith, this indicates that one has never been born of God.

See also A comparision of interpretations of 1John 3:9

Related Verses

I compare the Bible with what those of a Free Grace and Arminian theology would say.
Free Grace We have come to share in Christ regardless of whether we hold firmly to the end the confidence we had at first
Arminian We presently have come to share in Christ, but we will lose our share in Christ
if we do not hold firmly till the end the confidence we had at first 
Hebrews 3:14 "We have come to share in Christ if we hold firmly till the end the confidence we had at first."

We are presently saved if we happened to endure to the end. All three theological viewpoints acknowledge this truth. But to me what it implies is that "if" means "only if". For if it doesn't mean "only if", then almost any senario is true and the writer wouldn't really be saying much of anything. But for then "only if" case it would also mean that if a person fails to endure to the end, then such a person had never come to really share in Christ to begin with. Such an interpretation is incompatible with the Free Grace position, which makes no assumptions about future behavior. It is also incompatible with the Arminian position which makes no assumptions of a person's future behavior based upon past salvation status. For they say that if a Christian does not hold firmly to the end, it doesn't mean that he wasn't saved at some point, but rather that they lost their salvation. At issue is whether "if" means "only if". The same could be said of:
Free Grace We are his house regardless whether we hold on to our courage and the hope of which we boast.
Arminian We are presently his house but won't be his house in the future 
if we don't hold on to our courage and the hope of which we boast.
Hebrews 3:6 "But Christ is faithful as a son over God’s house. 
And we are his house, if we hold on to our courage and the hope of which we boast."

Let's consider also a similar verse:
Free Grace By this gospel you are saved regardless whether you hold firmly to the word.
Arminian By this gospel you are presently saved, but you can lose your salvation if you don't hold firmly to the word
1 Corinthians 15:2 "By this gospel you are saved, if you hold firmly to the word I preached to you.
Otherwise, you have believed in vain."

This contradicts the Free Grace position. But can be used to affirm Lordship Salvation. It could also support the Arminian position if we just focus on the present tense for "hold firmly". But even so it could not be used to reject Lordship Salvation. There are those who "believe", but not with the quality of faith acceptable to God for salvation. They believe in vain. They never were saved and thus the once saved, always saved doesn't apply to them. There is a faith that doesn't save. A non-application oriented faith is a dead faith of no saving value.
Free Grace But now he has reconciled you regardless whether you continue in your faith
Arminian But now he has reconciled you, but you lose such reconciliation if you don't continue in your faith
Colossians 1:22-23 But now he has reconciled you by Christ’s physical body through death to present you holy in his sight, without blemish and free from accusation— if you continue in your faith, established and firm, not moved from the hope held out in the gospel.

Once again if we interpret "if" to mean "only if", this again eliminates both the Free Grace position and the Arminian position. For what if ones does not continue in the faith? It's not that he lost his salvation. But rather he had never been reconciled to begin with. The verse speaks of a present and past condition (reconciled) in view of a future behavior, which as I pointed out above is incompatible with both positions and only supports the case of Lordship Salvation. And many other such verses can be interpreted in a similar manner such as John 8:31 "If you hold to my teaching, you are really my disciples." (And thus if you don't hold to his teachings, you really weren't his disciples to begin with)

At  issue in many of these verses is not so much once saved always saved, but how does one know whether one has ever been saved. For Paul even writes the Corinthian Christians saying:

"Examine yourselves to see whether you are in the faith; test yourselves. Do you not realize that Christ Jesus is in you-- unless, of course, you fail the test?" 2Cor 13:5

For more perspective on Lordship Salvation see:

The Berean Christian Bible Study Resources