Your question is a variation of this Meta and our FAQ:
The key quote is
All bounties are paid for up front and non-refundable under any circumstances.
Indeed, on Meta Stackoverflow this is described in detail and I'm quoting directly since it is succinct:
A bounty is not a guarantee. It's less risky in the new system, but it never has, nor ever will be, a guarantee for the answers you need. It's payment for a bid for an answer, not payment for actual answers themselves.
Remember that although you didn't get an actual answer, you did get 7 days on the Featured tab. If you got refunded, then you could keep your question on the Featured tab forever, which really reduces the benefit that placing a bounty has in the first place.
Basically, consider this like a parking meter - the reputation you spent is good enough for only 7 days. If you need more time, you need to spend more reputation. Of course, it's a parking meter where you can pay however much you want and get the same amount of time, but the extra payment is for the possibility of better quality attention during that same period.