It is a best offer so they will almost alway offer half, that's why you negotiate. When we get a best offer I usually take them, only because I paid under $5 for it and getting a really good price. Like today we have a buck display case on have it at $80 got a offer for 59.00 and it has a flat $20.00 shipping on it. Took it, is it a big cut, yes and no, we only paid 10 for it and well get a little of that shipping.
Truthfully auctions with bin are pointless. If you have a hot item and your hoping it will go above let say 100. Okay you start the auction at 50 with a bin at 80 and your hoping it goes to 100, as soon as it gets close to 80 it will most likely sell for 80. Who's going to keep bidding up above the cheaper price of 80, if they do keep bidding it up over 80 their dumb. From what I gather your running auctions with bin and best offers? Why, run one or the other. In our experience we have ran about 30 auctions and never 1 has paid, ever. Unless you have a hot desirable item just use bin.
Don't be afraid with bin to list high with a best offer for 30 days. You can always lower the price, get best offers or shorten the listing time anywhere up to 15 days into the listing. Also with bin you can put immediate payment. That way if they do make a offer it will stay listed incase you have other watchers they can still get the item at full or higher price. We all go through these bad buyer slumps. That's why eBay needs to allow negative feedback from sellers about buyers, it would avoid a lot of these very problems we all experience. Last I checked we as business owners have the basic right to refuse service. Good luck and hope it works for you.