I wanted to put a low reserve on to see if that would keep the BIN price available for a while. Couldn't find it.
IIRC the BIN stays until the reserve ends.
Being asked is an annoyance. If I wanted you to BIN I'd have put a sodding BIN price on the listing wouldn't I?
But the problem with eBay is that I often put a BIN price along with a 99p starting price. So if you see it and want it then you can still buy it. Once bidding starts then the BIN price disappears which is daft in my opinion. Fair enough, in the last 24hr its' gone or something.
So it depends how I'm feeling. If I think something will go I often refuse the BIN enquiry politely. Be patronising/internet warrior-like with someone whos asked a relatively valid question means one less potential bidder in my opinion.
I once had someone buy something for a mad amount of money then give me grief that she could have bought it off my at a cheaper BIN price. That was an interesting email I sent her back. She did pay up though...