Sometimes in situations like this, one can get more with honey than with vinegar. Calling up and saying, "Yeah, I know it's past the warranty. But I know that you're a good company and you want to stand by your products. I really like the product and would like to continue using it, and I would like to be able to recommend it to my friends. Could you please make an exception in this case?" (And if the flunkie on the other end of the phone can't, ask to be escalated, lather rinse repeat.)

I'm not saying this would work, I'm just saying that it's the first thing I'd try in this situation.