That sounds like a too short cable. What I described earlier was a situation where the cable was stretching, which would happen if it's too short and being forced into a tight bend when routed around a folded frame. At this point I'd recommend a new higher-quality shift cable-and-housing, maybe an inch-or-so longer. You don't want this huge loop of derailer cable sticking out when folded, but it needs to be long enough to keep a steady, smooth arc through the folding process. Right now it sounds like its being pulled and stretched between the shifter and derailer. Not good!