iPhone suddenly goes dead, then doesn't charge for 12+ hours

I have an odd problem I can't explain. A couple of times now, I've pulled my phone out of my pocket to find it completely dead. It won't turn on at all. I plug it in to charge and rather than getting the battery charging indicator, nothing happens. Resetting the phone by holding the Sleep, Home, or Sleep+Home buttons does not help.

After letting it sit for about 12 hours, I plug it in again to get the "battery completely dead" sign. There's a red line on the battery indicator, a lightning bolt, and it takes several hours to charge back up.

This has happened to me twice in about the past 6 weeks. I'm wondering if this is familiar to anyone else, because I have 3 weeks left on the warranty and am afraid it will die for good in 3 weeks + 1 day.