I had a problem sort of similar to this. I was romping in the desert with my completely stock 2000 SR5. It might be considered abuse, but I was flooring it around roads and small trails like it was a trophy truck and it handled like a champ (weak, V6 champ) and didn't break. However when I parked it back at camp and went to take it out next time, it would start. It sounded happy, but never kept going after taking it off ignition. Had no idea what was wrong, everything under the hood looked fine and the battery was relatively new and was turning it over plenty enough.

Then I thought, why not just gas it a little? So I turned it to start and gave just a little bit of gas and stayed on it (maybe 1000rpm) while I took it out of start and back into the On position. I let off on the gas, and it just idled like it normally should. That was over a year ago, and to this day I have no idea why it did that, but I haven't had the problem since.

So my advice is to take the key completely out, and then give it some gas when starting it. It didn't die mid-acceleration, but I have had the engine just turn off if I give it all the beans and then immediately let go of the gas. But that only happens if I hit the rev limit (5500rpm I think).

It could also be something more serious, but there's my 2 cents.