Along that same line, albeit the opposite direction.
I once did a project retrofitting a VFD and motor to replace a diesel engine driving a WWII era portable rock crushing machine (used for making runways in the Pacific). Everything worked great at first, but the longer the machine operated, the slower it ran until eventually it would just stop. Because I provided the VFD and integration, I was called to solve it. The thing was, the drive and motor were NOT slowing down, they were perfectly steady, yet I witnessed the machine steadily getting slower and slower. Everyone kept blaming my drive or my control system, but I was looking right at it, dead steady. I even put a hand held tach on the shaft to prove the motor was at the correct speed. Turned out of course that it was a belt drive system and the belts were slipping, which got progressively worse as they heated up. They were actually smoking, but the machine made so much dust that nobody could tell. I smelled the burning rubber, nobody else did but once I pointed them to it, it was very obvious. Turned out I had grossly over estimated the HP conversion from engine to electric even though my math was correct, because an electric motor develops torque instantly, an engine has to build it slowly. The belts that had worked fine for 50+ years couldn't handle that.
The point is, it's NOT automatically a control loop problem. By the way, I've experienced the fluid coupling issue too. I also had that on a magnetic particle clutch where voltage drop from the main motor drive was allowing the clutch to slip for years, then when I put in the VFD, I also changed the transformer and fixed the voltage drop, so the particle clutch fully engaged and the machine ran faster.