1 Corinthians 15:2, Colossians 1:23.
Best keep it in context what that belief and faith is about rather than the act of continuing to believe and keeping faith.
1 Corinthians 15:1Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand;[SUP] 2 [/SUP]By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
Colossians 1:[SUP]20 [/SUP]And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven.[SUP] 21 [/SUP]And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled[SUP] 22 [/SUP]In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight [SUP]23 [/SUP]If ye continue in the faith grounded and settled, and be not moved away from the hope of the gospel, which ye have heard, and which was preached to every creature which is under heaven; whereof I Paul am made a minister;
Former believers are still saved. They are at risk of being let behind for denying Him, but He still abides in them.
2 Timothy 2:[SUP]10 [/SUP]Therefore I endure all things for the elect's sakes, that they may also obtain the salvation which is in Christ Jesus with eternal glory.[SUP] 11 [/SUP]It is a faithful saying: For if we be dead with him, we shall also live with him:[SUP] 12 [/SUP]If we suffer, we shall also reign with him:
if we deny him, he also will deny us:[SUP]13 [/SUP]If we believe not, yet he abideth faithful: he cannot deny himself.
That is why we labor to call saved believers and even saved former believers to repentance or else be denied attendance to the Marriage Supper at the pre trib rapture event, thus excommunicated into the bed of the coming great tribulation to be received later on as vessels unto dishonor in His House as that IS where the vessels unto dishonor comes from that are in His House still.
2 Timothy 2:[SUP]18[/SUP]
Who concerning the truth have erred, saying that the resurrection is past already;
and overthrow the faith of some.[SUP] 19 [/SUP]
Nevertheless the foundation of God standeth sure, having this seal, The Lord knoweth them that are his. And, let every one that nameth the name of Christ depart from iniquity.
[SUP] 20 [/SUP]But in a great house there are not only vessels of gold and of silver, but also of wood and of earth; and some to honour, and some to dishonour.[SUP]21 [/SUP]If a man therefore purge himself from these, he shall be a vessel unto honour, sanctified, and meet for the master's use, and prepared unto every good work.
So the exhortation to continue to believe and to keep the faith is not for salvation, because they are saved, but for being received by Him as a vessel unto honor in His House.