I encountered the same problem both the front and rear lights and contacted them since there was a lifetime warranty.
I inquired in October 2012 and have been told that they were out of stock and order would come in 12/07/2012. It was late but I said ok and returned the defective lights. Today, December 13th, I sent a follow up email to see the status and I have been told that the the product won't be in until January 7th 2013. i wonder what they are going to say in January when I ask for the status. February 7th, March 7th?
Anyway, this is my experience with the return/exchange with Blackburn Design (not Amazon). Even though, I like the look of the product, I won't buy it again or recommend it. There are many competitive products out there, most likely better quality and hopefully with a better customer service.
I have had two Blackburn Flea rear lights fail after only a few weeks of service. I returned the first one, and the second promptly failed in exactly the same way - it would turn off without me pressing the switch. I was curious, and I am an electrical engineer, so I decided to sacrifice the $30.00 and open the light ( you can't open it without destroying the shell ). I found out that the battery hangs from a tiny solder joint which breaks, causing the battery to lose it's connection to the circuitry. The breakage appears to be from repeated impacts as your bike goes over bumps, causing the weak solder connection to fatigue and fracture. If you tap on the light, the battery may temporarily make contact through the broken solder joint, causing the light to work again, only to fail again after you hit another bump. In my opinion this is a major design defect in the Blackburn Flea. The front light appears to be less prone to this failure since the battery is sitting on the solder connection rather than hanging from it.