Salvation is Whosoever, but is it whensoever?

I've heard that salvation is a "whosoever" salvation which is clearly Biblical, but is it a "whensoever" salvation? I heard stories where one was convicted of sin by the Holy Spirit, and that he did not get saved, he was going to wait for the next time this happened, and it took almost to near the end of this life to happen again. This is a cute story, but is it Biblical? Opinions MUST be backed by scripture. Thank you :)