Although it's frustrating that the winning bidder wants to back out of the transaction at least she's had the decency to tell you now, rather than just pay for the item and then invent some silly reason to return the item for a refund. By handling the situation in the way that she has this buyer has saved you from a lot of further aggravation, as all you need to do is cancel the sale and the sale then becomes null and void.
Given that the winning bidder has e-mailed you via eBay Messages to explain that she no longer wishes to buy the item just cancel the sale via eBay, citing "The buyer and I have agreed to cancel the transaction" as the reason why. That way the sale will be cancelled and you will get your Final Value Fees back again.
With regards to the part of your query where you said "However, that means I have to relist it, and wait to send it again" you don't neccessarily have to relist the item. Go to your My eBay, click on the All Selling tab, then scroll down the page until you find the item in question. On the right of the screen there will be a "More Options" menu. Pull up the drop-down menu and click on the "Second Chance Offer" option. This will then give you the chance to send a Second Chance Offer to one of the bidders who lost the auction. If the person to whom the Second Chance Offer has been sent decides to buy the item then you will still end up with a sale, albeit for slightly less than you would have got if the winning bidder hadn't changed her mind.
Finally, with regards to making a Second Chance Offer to another bidder it's OK to do so, provided that the original transaction has been closed down first, whether via a cancellation or an Unpaid Item Dispute being opened and closed without payment. An Unpaid Item Dispute can take at least four days to conclude, so I'd go for the former option in this instance.
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