02 mirage with A/C problems

The A/C in my 2002 Mirage works fine for about 20 min. then starts blowing out hot air. If I shut it off for about 20 min. then turn it back on it will start blowing cold air again, but only for about 15-20 min. The refrigerant level was check out and was ok. Also the system isn't leaking. When the a/c works it blows out cold air. Can anyone help me with this problem? Could this be the compressor starting to fail?

When it stops blowing cold air, is the compressor clutch engaging?

When it stops blowing cold air the clutch isn't engaging at all.

I noticed last week when it was below 90° outside that it ran a little longer before stopping. (20-25 min.)

If the compressor was bad wouldn't it not work at all? When it does work the air seems very cold.