To confirm, the problem is not holding position to keep the chain in the larger cogs in back.

the most probable issue is at the shift lever.
not holding tension. As it is a Spidel rear mech a decent chance it has retro friction shift levers
if so, internal parts can wear or fracture- this would be the easy to assess and expensive to repair- no parts any more- one would have to buy an assembly. Regular friction levers would work too and be cheaper.