Air condition Problems

There are a couple things that come to mind when doing this. However, the thing to start with is to check the pressure in the system.

Even though you are getting cool air on the lower settings there is a chance that we have an issue with the pressure that is causing the compressor to cut off when you are setting to Max AC.

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

Assuming the pressure is ok, we could also have an issue with the pressure cycling switch, so we are going to have to jump the switch and see if the compressor comes back on.

However, let's start with the pressure and find out if we have an issue here because if we do then we need to go a different direction.

I am attaching a chart below that will help with determining if this is an issue.