It’s not biblical at all and does just what the author says.
Hebrews chapter 6 puts the nail in the coffin of once saved, always saved:
Heb 6:4 For it is impossible for those who were once enlightened, and have tasted the heavenly gift, and have become partakers of the Holy Spirit,
Heb 6:5 and have tasted the good word of God and the powers of the age to come,
Heb 6:6 if they fall away, to renew them again to repentance, since they crucify again for themselves the Son of God, and put Him to an open shame.
That scripture is talking about repenting back to Judaism...which is what the whole passage is about.
The writer was saying that it's impossible for a true believer to go back (repent) to Judaism which is what those people were tempted to do in the face of christian persecution. The book was written to Jewish believers (thus the title of "Hebrews"). It's all about the futility of the old Jewish practices.
No, that is not what the passage is talking about. Read the way you are saying it DOES put a nail in the coffin of there EVER being the possibility to repent, confess and return to the faith. If you notice, the verse you gave says it is "IMPOSSIBLE... TO RENEW THEM AGAIN to repentance". So, by this way of looking at it, you get ONE chance to be saved and if you screw it up, you can NEVER come back. Are you sure this is what you want to say to people, people who have a sin nature?