Mazda Miata Compressor -Engine Ignition Problem


I am the happy owner of a 2001 Mazda Miata with 111,000 miles on the odometer. I’m having a problem where if I run the fan/air conditioning compressor in stop and go traffic, the engine will sputter and die. It will not restart for some 3+ (with fan off) minutes after it dies and does so with the engine/ignition light on. If I shut the engine down again for dome 3 minutes, (w/ out engine/engine light) the car starts and runs normally. The same thing happens if I am running the car in a non traffic situation with the fan, but not the compressor. The engine sill lose power and die, forcing me to go off the road and restart the above process.

My mechanic is at a loss. H originally thought I had a dirty fuel line and gave me some chemical substance to clean it, but to no avail. The problem starts again.

Please help. Summer is here and Houston is both HOT and HUMID and w/out air conditioning, I am sweating profusely by the time I make it in to work. THANK YOU!!