It depends on a piece of information which you cannot normally find out: Was the winning bid, which fell through and resulted in the second-chance offer, just a random deadbeat bidder? Or was it a confederate of the seller (perhaps the seller himself in disguise) shilling up the auction to test what your maximum bid was?

In the former case it is fair for the seller to offer what he did, although I think you'd have some negotiating room if the spread was large (remember he has some motivation to get the item sold and his winning bidder just defaulted.) In the latter case, the seller is using his shill to try to cheat you out of the difference between your maximum bid and the last bona fide bid. The mere fact that you got the item at the maximum you were willing to pay has nothing to do with this -- it's still fraud. eBay's discussion of shill bidding makes this very clear. (Whether you love eBay or hate it is immaterial. Shill bidding is fraud commited against legitimate buyers.)

As I say, you usually can't know why the winning bid didn't win, so you have to go with your gut, depending on how badly you wanted the item. If you think you may have been shilled, you have to ask yourself, "Do I want to deal further with a thief?" If the seller offers to take payment outside PayPal then you know for sure he's trying to cheat eBay, so odds are he's trying to cheat you as well.

Edit: I've accepted second-chance offers, too, and have been happy with the results. My father worked in retail all his life -- there are a lot of bad customers out there and I sympathize with sellers who have to deal with them. Fortunately most buyers and sellers are trustworthy.