Falters (Hesitating) with gentle gas being applied

I am so frustrated, I've always had my car dealer maintained, and now after 3 trips to them, they cannot determine what is wrong with it. The 2nd trip was just a bust because they couldn't duplicate the faltering.

Details: Slow/gentle gas causes car to falter.

When the engine is warm, it falters when leaving a stop and only with low/ gentle gas being applied. It is a very noticeable falter, even when traveling at 40-50 MPH, when I apply the gas pedal gently just to maintain that speed, I can feel it faltering. However, when I take off from a stop with umph or give it steady and strong gas at higher speeds - no faltering.

It has never stalled or not wanted to turn-over/start.

What the dealer has done to date: cleaned the EFI twice Oct 11 and Mar 12; replaced the fuel filter; replaced the air filter twice Oct 11 and again last week Mar 12; top engine cleaned to include the throttle body; flushed the transmission fluid; repaired transmission cooler line (it was leaking).

I purchased the car new. Other than this issue which only started last Sep, it is a great and reliable car. I hope to have it for another 150,000 miles.

Appreciate your time and help!