What happens to questions which have been on a tie break for a long time? Say three weeks or more?

they stay tied till someone else votes and there is a best answer

They hang in limbo until the tie is broken. There are some that have been in voting for a year or more. I've gotten best answers from questions I'd answered a year ago because the tie was finally broken.

They stay there forever, or until someone breaks the tie. I've gotten Best Answer notices from questions that were over 1 year old, before!

the question remain in vote until the next vote comes in to break the tie breaker

They just sit there.

Some time ago someone claim to have got one that was a year old.

see the little green box that says undecided!! thats where they are