Notice how John warns the remaining believing ones to not do the same thing but rather let the word of the gospel remain in them:
1 John 2:24 NASB
24As for you, let that abide in you which you heard from the beginning. If what you heard from the beginning abides in you, you also will abide in the Son and in the Father.
Do the many Bible references to keep believing in the word mean believers can potentially return to their old lives of unbelief, or are the warnings sufficient to keep every 'real' believer in the word? Besides the warnings being so pointed, Jesus does talk about little ones who believe in Him stumbling and going to the eternal fire in Matthew 18:6-9. This suggests the problem isn't the difference between fake faith and real faith, but rather weak faith vs. strong faith.
Okay, good. Then you agree that works must accompany salvation. Not to secure justification, but as the expected outcome of the person who has faith in Christ.
But to the point of your post. 'Temporary' belief can be qualified as 'weak' faith, not just 'fake' faith. It's genuine, but it's weak, and because it's weak it withers before it comes to maturity. The misunderstanding of the 1 John 2:19 passage (which by the way doesn't have the word 'really' in the original) seems to be the misguided energy behind the prevalent thinking in the church that failed faith is always and without exception fake faith. But there is certainly Biblical room to consider that failed faith can simply be weak faith. Weak faith that can't stand up to the trials and temptations of this life but is easily drawn away in favor of a return to the old life.