A 1 Watt luxeon requires 3.5V drop. The question you should ask is how long does it take a the battery pack to droop below 3.5V when supplying 0.35 Amp. At that point the LED driver circuit would have to start throttling back the duty cycle (brightness) to maintain 3.5V across the LED. Then you have to ask how much does the brightness have to decrease for it to really matter? If my EL500 were running at half its normal brightness I would still be doing just fine.

The EL500 contains 4 AA cells, so each cell would have to droop below 1V to start throttling back the duty cycle. At 1V NiMH cells are over 90% discharged anyway. I use 2000 to 2250 mAH NiMH cells. The 2000 mAH cells can supply 0.375 amp for about 5 hours. (Note that NiMH cells maintain their voltage better than alkaline under load - that is, alkalines droop faster and deeper but have more mAH per discharge.) The 4W halogen the above person is so fixated on would produce about 4 times the brightness and exhaust the batteries at least 4 times faster. (4W/1W = 4 for those who can't divide) Personally, I DON'T need 4 times as much light, but I DO need 4 times as much battery life. That's the trade-off we all have to decide for ourselves.