If a bike goes into repo is a there a time limit in which the title becomes clear if the bike is never recovered?

No. Once in repo, they don't just forget about it.

Call them up and give it back... as Odinn7 states... you don't get to keep it for free... its theirs.

The title shows the finance co. bank, or whatever as lienholder, right? The only ways the lienholder can be taken off is either to pay off the lien, or if the bike is repossessed and re-sold.

Not only will the title never clear, but the repo man will always be looking for it. No matter where its hidden.

If a bike goes into repo is a there a time limit in which the title becomes clear if the bike is never recovered?

If you are thinking that, some time in the future, the lienholder will be cleared off the title, then you are very mistaken. A debt never expires.