On older cars the wipers were run by a mechanical arrangement under and in front of the dash, and when one wiper went limp, it meant you had to reach around in there and pop the wiper arm male connection back into the drive mechanism bushing (a rubber donut affair). Once you did it the first time the next time was easier. Mine usually only popped out if there was heavy snow or ice on the windshield adding an unusual load to the system.
On the W126 model I owned, this was sadly changed to a modular unit in the area of the base of the windshield. The design was not as robust, and when it let go of one of the wiper arms, it usually meant the bushing, now made of plastic and held in place by a large sheetmetal stamping, broke, and there is no provision for replacing just the bushing. I tried several solutions that did not work before I gave in to the new mentality and bought a new assembly, which included the motor. It cost me several hundred dollars to have the whole unit it replaced.
It is possible yours is not really that bad if it sometimes works, but I would not hold much hope. Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)