It takes a while for the air conditioning to cool a car down. It isnt immediate. We had one guy that said his AC wasnt working well. First I discovered all of his windows were open about an inch. I hope he wasnt expecting the AC to work well with the windows open. So I closed the windows, and put the AC on. I left a thermometer in the car, and after 15 minutes, it was 50* in the car. I dont know how much better the AC in an 8 year old car is supposed to work, but 50 is pretty cool.
The reason it seems the AC doesnt get really cold on sweltering days is because AC has a tough time cooling when its hot and humid, much like humans do. AC works by (this is simplified) removing the heat from the air in the car and sending it outside. Stand next to the outside part of a working home AC and you will feel that its very hot. The problem is when the AC is trying to put hot air into the outside air that is already very hot and humid.
You know how much hotter you feel when its very humid? You sweat and sweat but you dont feel any cooler? Humid air is air that has a lot of water in it. Your body cools when your sweat evaporates from your skin into the air. But humid air cannot accept the water from your sweat because it is already holding so much water. In hot but dry air your sweat can evaporate easily and this cools you (I saw this explanation on the weather channel).
Your AC works in a similar way (again very simplified). It has a hard time getting rid of heat into heat. So it doesnt work as well.
Theres another factor, and that is the heat of the car. Your car feels the heat too, and the engine radiator is working like crazy trying to get rid of motor heat into hot outside air. The engine compartment is hot like an oven, and unfortunately, the AC heat exchanger is under the hood, RIGHT NEXT TO the blazing hot engine radiator. This is a result of packaging constraints; the AC components need to be located somewhere near the motor. But it doesnt help.
So in summary, its hot. You put on the AC, but ironically, it works less well at the very time you need it to work best. This is probably better explained by the laws of thermodynamics, or the conservation of matter and energy, or something complicated. But your AC is probably really working, even if it seems like it is not.