Does the fan continue to blow, but the air is no longer being cooled? Or does the fan slow down or stop? It's not exactly clear which problem you are experiencing.

It sounds as if you have the classic 124-chassis-ac-cutout-problem. It's been discussed here a million times. Briefly, your car has a circuit which compares the speed at which the a/c compressor is turning to the speed of the engine. If there is too large a difference between the two, the system assumes there is a problem with the a/c compressor and shuts it off to preserve the single fan belt. The compressor remains shutdown until the ignition is recycled. About 99% of the time there isn't a problem with the compressor.

Try searching this site using phrases such as "compressor cutout" and "klima relay" - you'll receive quite an education.

Here's my short list of possible causes:
1) Worn/dirty/stretched serpentine fan belt
2) Defective serpentine belt tensioner
3) Compressor clutch dirty/oily
4) Compressor clutch gap outside specification
5) Defective klima relay
6) Intermittent connection between compressor RPM sensor and klima relay
6) Intermittent connection between engine RPM sensor and klima relay

The good news is that none of these problems are too expensive to cure. The bad news is the challenge in determining exactly which one(s) your car suffers from. I too own an '87 300TD and, as you can probably guess, suffered from intermittent air conditioning. My specific problems were #3, 4, and 5 from the above list.

Oh, if you mean the fan stops blowing any air into the interior, cooled or not, then ignore the above. One possible cause of this problem is a defective ignition switch. Try jiggling the key to see if the fan comes back to life.