If a refund is in order you have to make the option of a full refund available if requested. One example is when an item fails within its guarantee. You can however suggest alternative choices before they request a refund.
Items have to arrive in the hands of your customer to their satisfaction and met the description including guarantees before it can considered their responsibility in any way, under distance-selling businesses regulation. Non-disposable/perishable goods sold over a distance must come with a 30 day guarantee.
A good introduction to the law is available on the eBay policies page
After compensating your customer you should look into claiming on the original guarantee of the product when you purchased it. You may be in time to claim on your guarantee. If not then it will be one of your business expenses. One of potentially more, so its standard to have protected funds prepared for this purpose beforehand.