Yes.
Basically, if you did not use Delivery Confirmation /tracking and cannot prove that the item was delivered, you should refund the buyer.
If you don't, she can go to Paypal and have the entire payment refunded by them and then PP comes after you. You also will have a violation/defect on your selling account.
Try to persuade the buyer to wait until Day 30 for delivery. Then if nothing is delivered by Day 29, refund and write the loss of your fees and purchase price (not of your markup which is an illusion at this point) off as a business expense.
My customer base is very honest and I rarely have to make such refunds, once or twice maybe since 2001. But philatelists, bookworms, and seamstresses are detail oriented and read carefully. Your Mileage May Differ.
Use Delivery Confirmation/tracking on items you can't afford to lose.
