The A/C compressor is driven off the accessory belt and only operates while the engine is running.
In normal auto-stop/start conditions, the evaporator cools down quite a bit while the compressor is able to move refrigerant through the condenser/evaporator loop. This cold evaporator continues to provide some residual cooling after the engine (and compressor) stops, as the HVAC fan (electric) blows air through it. However, the length of time you can get cool air depends greatly on the ambient temperature -- hotter ambient air will rapidly heat up the evaporator and you're left with effectively hot ambient air being blown out the air vents.
In extremely hot conditions, I would expect the A/C to effectively be non-functional while the engine is not running, as hot ambient air quickly re-heats the evaporator. To stay cool you really need the refrigerant to flow, so heat can be taken out of the air by the evaporator, transferred to the refrigerant, and carried to the condenser, where the heat is dissipated to the outside air -- ideally through the massive amount of air rushing through the condenser as you drive down the road -- but augmented by the electric cooling fan to create airflow while in traffic or otherwise stationary.
On really hot days, if you want consistently cool air -- even when sitting at a stop light -- then you'll have to turn the engine auto-stop/start function off. This will keep the compressor powered and your A/C working.
Long-term, I'd like to see more vehicles move to an electric A/C compressor. This would decouple the A/C system from the engine and allow cooling to work without the ICE running. This would solve the "hot in traffic" problem, as well as allow vehicles to "precondition" their interior air while in enclosed garages/areas without running their gasoline engine.