One problem with bounties that has turned me off using them is that if you start one, you will have an answer selected and you may not get any good ones. I can understand the bounty having to end to stop gaming the system but maybe we need some flexibility here?
Perhaps we should allow the OP to pay in extra to extend it another week, a few days or whatever. This should only go on for so long. Maybe a month total? Arguably this extra rep added shouldn't increase the bounty either.
Maybe the amount to extend it is also a function of the size of bounty?