@Vincent.
If your flashlight died out after a few weeks in the way you describe -- it's either got a remarkably insufficient resistor, or (far more likely) it was a Dollar Tree Special that doesn't have that protective component at all (I got bit there once myself). The light in my pocket came with a Rayovac AA for ~$5, and has served me well for a year or two now.
It's not my all-time favorite (that would be the Brinkmann one that I had until it died... a replacement is $20, to which I say, "I don't think so, Tim!") but it's very nice. It's this one here http://www.ebay.com/itm/331836187844. I'd buy that, even though it's $3 more than I paid at *cringe* Wal*Mart. (For the record, mine is a sort of bronze-ish color, almost a dark gold... not silver like that one.)
@ Luke. 20mA @ 2-3.5v, depending on the LED in question and its color. eBay-issue cool white LEDs are 3.4v... I have a bag of 50 warm white ones that are otherwise identical... I'd be inclined to call 40mA at 3.4v (quick mental estimation pots that at ~1/8w) fairly trivial for an average vreg, but i'm just a hobbyist -- I'll defer to you on this one, since you're the resident expert.