We have a tractor which has worked this way for a while...

Turn on the A/C & set the thermostat for some cooling and you get cooling...for a while.  Eventually you realize the fan is blowing warm air.

So you turn the thermostat cooler and cooling resumes...for a while. When warm air comes again, you repeat turning the thermostat cooler...

...until you eventually have it on max cooling. And that works for a while, but when warm air blows again there's no more thermostat range available, so you turn off the A/C altogether for a while. If you wait long enough, you can again turn on the A/C and run through the whole cycle again, except now the system is warm so you get to "no cooling" much quicker.

This isn't too bad in moderate weather, but the hotter the day the more of it you spend with no cooling.

What things to check?  Too much freon?  Bad high limit switch? Expansion valve problem? Other?