Probably the regulator. Only way to see what's happening is to pull the inner panel of the door and have a look. You can find aftermarket (Chicom) regulators on ebay for relatively cheap, I put one in the right rear of my car and it has been fine for years. Here is the thread on my rear door regulator replacement, the most difficult thing for the front is getting the seat control switch off without breaking it, no tips other than "pry carefully".... If you break it you can find a used one somewhere on line.
Let's pull the rear door panel on a W124!
Rgds,
Chris W.
'95 E300D, 399K