So sorry this happened Bayne. I can't tell you what to do, but ask some things that may helpyou make a decision. Have you considered what is financially less loss for you, to refund or to re-mail, this time with insurance or through a global carrier such as UPS? Maybe ask the buyer to cover the upgraded shipping?
USPS does not track packages once they leave the US, and in some cases packages have been lost or stolen before arriving to the addresee, and in some cases adressees feel it's okay to claim for their money back using false information. Can't say what really happened here, but if the buyer says this happened to them before that raises a red flag to me. If they are sincere and honest, they may be willing to pay for shipping insurance, since you have proof that you mailed it in good faith.
Another thing, how did they pay you? Paypal covers buyers. I believe for 45 days. Did buyer just report the unreceived package recently? If so, why did buyer wait so long?
What recourse does buyer have against you? What are your store policies, do you refund or only exchange? And again, what are you more willing to do, what is better for your business?