nailbender
Flashlight Enthusiast
I would expect that if the heatsinking was marginal it would show angry blue, and possibly be damaged rather than so quickly destroyed. Since it goes completely out rather quickly perhaps the current is waay too high, and it isn't a heatsink issue. The OP didn't mention heat, if the light was used for short periods then overcurrent is more likely. If for long periods then heat buildup is more suspect.
In either case the "J" bin will reduce the current and likely solve the problem. One graph I looked at showed current doubling for 0.2V of change (with zero circuit resistance).
Here's what I'd do:
Install a J bin. Make sure the thermal epoxy is thin, and double check the electrical isolation.
Measure the current at the tailcap. If over 2.8A add some resistance (probably won't be needed).
I agree with alan, I think the most important thing is to make sure the AA is thin and the LED is well attached. I use three 10000 mah NIMH batts all the time and never have any trouble. They are all direct drive and I test all for at least 45 minutes. I just sent one to CA and the member said he ran on high for over two hours. If there is the smallest crack between the Led and the heat sink or the adhesive is too thick it will heat up and turn blue.
I have seldom measured more than 3amps for extended periods of time from three NIMH.