+1 - I'm running a built a340le (jdm-soarer version, same thing), lotsa hp...no problems.
Word to the wise - what I am refering to (as well as IJ, I'm sure) is a fresh, fully and correctly built, healthy, auto trans. I've got kevlar clutches, shimmed accumulators w/ heavier than stock springs, high performance pump etc.
If you are putting big hp into a high miles, worn trans w/ bad seals etc., expect problems as you would in any transmission in that condition that you are putting more strain on w/ additional hp.
The a340 gets a bad rap in my opinion. It's a very sturdy transmission.
I would only consider swapping in something else (namley a th400) if I decided I wanted to go with a trans-brake for drag racing, the fact that I even consider the need for one should give you some idea of how badly I abuse my a340. Unfortunately, a trans-brake cannot be done with the a340. Other than that it's all good.