'03 Honda Civic stalls, or almost stalls

stall
honda
#1

Over the past 2 months, very sporadically, my '03 Civic (31,000 miles) stalls, or almost stalls while I’m driving. Mostly, it almost stalls - quietly and suddenly. It feels as if all of a sudden, it’s not getting any gas or the car is shutting down. But when I floor it, that prevents it from stalling. Sometimes it only happens once, sometimes multiple times. Always, it has been when driving locally, usually about 10 minutes after starting. I’ve taken several long car trips without this happening. My mechanic (who came highly recommended) is stumped. They cleaned the throttle body, but it didn’t help. He has also experienced the problem, while he had the computer hooked up, but even as it stalled, the car gave no indication of what the problem was - no check engine lights or anything. This is the first problem I’ve had with this car - otherwise very reliable. Any advice? Thanks!