The climate control/AC control in these cars isn't a simple on/off system -- they have "smart" relays an controllers.
There are several possibilities:
No freon in system due to large leak
Defective expansion valve (cool but not cold)
Stuck heat valve, so the AC is working but the heater core is hot, too.
Are you sure the compressor is actually engaged, not just engaged for a few seconds then shut off? These units have a speed sensor, and if you have the wrong unit, the Klima relay shuts off the compressor after a few seconds. The 300E compressor is NOT the same as any other, and there may be model to model differences as well as year to year -- if the wrong one is installed, it won't work since the relay gets the wrong signal.
Working pressure should be 30 or so psi on the suction side, 300-400 psi on the hot side. You can check easily -- the suction hose should be cold and have condensation on it, the hot side should be almost too hot to touch. If not, the compressor isn't compressing or isn't running.
My indy mechanic has had fits getting functional rebuilt AC compressors, and any failure is always due to "dirt in the system" -- he installs a filter in the suction line. This is a dodge to sell crap rebuilds and deny warrenty (the latest swindle in the auto parts business).
My guess is a compressor/Klima mismatch -- do you have the number off the original compressor? You cannot just change the sensor, either, the relative speeds must be correct. Big pain. The mechanics have absolutely no idea how this system works, and since the compressor initially kicks on, they think it is fine. Find out which compressor you should have, and what was installed, and if they are different, get the correct one. May solve your problem. Also, do you have the original pulley on the compressor, or did you get one with the replacement? The wrong size pulley will do the same thing.
Also, high/low pressure switches can fail, so no compressor clutch engagement. Clutch can get oily or be out of adjustment and not turn the compressor, which will cause the relay to shut off, too.
Check auxillary water pump operation, too -- if it is stuck on, you can get excessive heat, making it look like the ac isn't working.
Not fun. I wish MB would sell the simple AC systems -- I don't mind setting the temp and function manually, saves a whole lot of hassle just to keep the car the same temp all the time!
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!