This is a very tricky one. Is the item very expensive? I have had a few, very rare cases of items going missing, so it is not beyond the realms of possibility that your buyer is telling the truth.
I don't think your buyer would have any reason to neg you if you sent a refund as long as you have kept in as regular contact as you possibly can, but I don't think they'd be happy to leave you positive feedback before they get their refund.
I know what you mean, the seller loses out if the buyer doesn't purchase insurance

it's a crazy old world. I tend to insist on sending anything over £30 insured where possible and I'm sure this puts buyers off, but I'd rather that, than lose an expensive item outright.
Sorry about all this