There are a few variables here that I was thinking about:
- Spend rep to extend a bounty for a certain amount of time
- Allow the rep spent to extend duration to add into the original bounty
- Create minimums on the amount necessary to extend dependent on how long it has been up
These are just ideas and can be tweaked as necessary, but the idea in whole is to encourage people to spend more on rep and avoid "wasted" rep because there wasn't a good answer to a question while minimizing the amount of possible abuse. This was part of the idea to spend a small amount of rep to extend duration without adding to the rep so that you wouldn't have to spend the whole amount over again for a couple more days.
The typical use case that I am thinking of is when you create a bounty and it still gets no attention. I think it would be cool if you could then add onto it to turn it into a higher bounty instead of having those points completely gone.
- Keeping bounty questions alive for inappropriately long times.
- There is already an answer but the author does not want to award the bounty.
For 1, you can resolve this by increasing the amount necessary to keep a question alive exponentially similar to what is already in place. You could also halve the amount of extended duration per extension. For 2, this is a problem with the existing system as well, but the author does not have a positive incentive not to award the points since he himself still cannot get them back.