Romans 8:12-13 Therefore, brethren, we are debtors, not to the flesh, to live after the flesh. For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live.
Notice that this is said to "brothers". If you live after the flesh, you shall die. If you live after the spirit, you shall live.
1 Corin. 9:27 - 10: 6 1 Corinthians 9:27 But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway. Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea; And were all baptized unto Moses in the cloud and in the sea; And did all eat the same spiritual meat; And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ. But with many of them God was not well pleased: for they were overthrown in the wilderness. Now these things were our examples, to the intent we should not lust after evil things, as they also lusted.
To the intent that WE should not lust after evil things as they also lusted.
As a Protestant, the idea was given to me that if a person really could not keep from sinning, then he really was not a believer in truth, but had just made a "head decision" for Jesus. Yet St. Paul shows us that we still have both an old nature and a free will which is capable of following evil, if we so desire to do.
1 Corinthians 15:1-2 Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain.
This is pretty strong also.
2 Corinthians 5:20-6:2 Now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God. For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him. We then, as workers together with him, beseech you also that ye receive not the grace of God in vain. (For he saith, I have heard thee in a time accepted, and in the day of salvation have I succoured thee: behold, now is the accepted time; behold, now is the day of salvation.)
I could keep going. There is plenty more to show that one may fall away.
Now, just to confuse things a bit -- I was surprized to find that the Catholic Faith teaches and acknowledges that there is an "elect of God" who will NOT fall away from the Faith, but will be kept faithful unto the end. What we are not allowed to do is to believe that we are personally among the elect unless we receive a personal revelation from God that this is so. This is called the "sin of presuming on the mind of God"
The problem is, again, that Protestantism has defined becoming a believer with being among those who persevere to the end. But entering into the kingdom, making a covenant through baptism, is NOT the same as inheriting eternal life. So it is possibleto reject the covenant relationship and leave the Faith.