This is called the “Once-Saved-Always-Saved” (OSAS) doctrine. A more thorough analysis of this false teaching can be found here.
One verse that squarely contradicts OSAS is found in Hebrews 10:
If we deliberately keep on sinning after we have received the knowledge of the truth, no sacrifice for sins is left, but only a fearful expectation of judgment and of raging fire that will consume the enemies of God.
The writer is talking about saved individuals here, not unsaved sinners. He goes on:
Anyone who rejected the law of Moses died without mercy on the testimony of two or three witnesses. How much more severely do you think a man deserves to be punished who has trampled the Son of God under foot, who has treated as an unholy thing the blood of the covenant that sanctified him, and who has insulted the Spirit of grace? For we know him who said, “It is mine to avenge; I will repay,” and again, “The Lord will judge his people.” It is a dreadful thing to fall into the hands of the living God. NIV (Heb 10:26-31)
Proponents such as Dr. J. Vernon McGee tap dance around these verses with elaborate arguments. They say a person can lose their reward but not their salvation. Verses such as 1 Cor 3:14, 15 do support that concept, but it doesn’t support the idea that one can never lose their salvation. God is not going to drag someone into heaven who doesn't want to be there.
