Dispute over item how to close case

[a1996k]

I have been selling on ebay for years now and have never dealt with a buyer claim until now. I have a buyer claiming her item never showed up. In order to try to avoid conflict, I told them I would refund them what they paid for the item since I do have proof of paying for the shipment and therefore sending the item (there was a mess up and I ended up without a tracking number but I have in my bank statement I paid x amount to the post office the day I marked the item shipped.) I issued the refund through paypal. However, now I am unable to close out the case and the buyer has been extremely difficult to work with and probably won't do so themselves since they are very adamant the shipping is refunded as well. What can I do about this situation? Also, what happens if the case never ends up getting closed or ebay thinks I have not responded in time? 

Sorry, if this information is available elsewhere but I've been searching for a while and cannot find answers.

[ma-647837]

Your buyer did not receive the item: You owe your buyer a full refund. Click refund in the refund request, and eBay will refund the rest of the payment you have so far partially refunded at PayPal.

Or to earn a defect, click Ask eBay to step in and make the decision for you. If you wait 3 business days, your buyer can themselves ask eBay to step in instead.

Then pray that your buyer does not reap you a negative donut.

[disneyshopper]

If you cannot produce a tracking number showing the item has been DELIVERED, then I suggest a full refund of item price + shipping.  Once you make the refund, the case should close.