I've never had that happen to me, but I tried to put myself in your shoes, and I think I would send a Second Chance Offer to the next-highest bidder. Hopefully they accept, and you're all set. I would do that without contacting the winner, or letting him/her know what I was doing, until after the fact. If the next person doesn't accept, you could always put a little pressure on that you tried that option, it didn't work, and as the original winning bidder they are in a binding agreement to complete the purchase.
What is the winning bidder's feedback like? If it's good, then their reasons are probably valid. If it were me, I'd likely just drop it and relist. If this person has done this to others in the past, then I'd block them from bidding on my stuff again.
These eBay situations can be sticky but you'll get through it! Good luck and let us know how it turns out.