One common cause on R129 (SL500 included), as well as W140 S classes is the HVAC shutting off. Without much to go on it is hard to diagnose. If the HVAC modules reads an incorrect temperature it will shut off as a failsafe. Little known fact is that a temperature sensor exists for the evaporator. A simple $35 replacement part could end up causing thousands in repair troubleshooting and possible unnecessary repairs.
There is a way to troubleshoot faults for the AC within the actual AC panel in the newer versions without the need of special DAS Mercedes multiplexer and software.
You can see what the original looks at the top and the OEM replacement under it. No need to get the Mercedes part for three times the cost.
To get to the sensor can be a bit tricky. You have to remove the soft cover under the steering column. This is a picture with it off.
The sensor can be seen in the picture below. Simply pull it out and replace it.
If you have a DAS engine faults reader, make sure to clear and HVAC codes, temporary and stored. The AC should start and not shut off now as the correct temperature is measured.