delayed notification – do i need to refund?

so a customer has just requested a refund (well, replacement but i am now out of stock), their product apparently hasn’t arrived, but it was posted on 48h delivery about 3 weeks ago. it was posted in uk with royal mail and it is almost unheard of for them to deliver to the wrong address, plus they will always try again the next day or leave it to be collected from a local sorting office.. so i am not sure i buy this not having arrived..

this is a high markup product and requires a lot of packaging and labelling, which is another reason why i am loath to refund

so my question is as follows: is there a statute of limitations as such on notifying the seller that your order hasn’t arrived? is there a time period after which the buyer can no longer expect me to fork out for a refund? i appreciate that this sounds stingy but we are a small business, and as i said this is a high markup product

ps. i know it is silly to offer a shipping option without tracking, it was a mistake and i have subsequently removed this option