So I did some experimentation with the Rover.
I used two configurations of the Rover.
A. Was just the front cab.
B. was the Front cab, Mobile Processing lab, and the Karibou Wheeled Storage bay.
With configuration B I tried parking it near the KSC runway. When I switched to a base on the mun then returned to the space center the crew went MIA and the ship remained where it was.
I then hyperedited another B over to another continent to see if proximity to KSC caused issues. But the same thing happened.
Finally, I hyperedited the ship into orbit around Kerbin at 100 km. The ship and crew have remained in orbit through multiple hours of play and multiple scene switches.
With configuration A I started by orbiting Kerbin. The crew stayed in the ship and the ship was fine.
I then moved it near my base on the Mun. When I returned to the Space center the craft fell through the Mun and the Kerbal was KIA
Later, I realized I never did a run with A sitting on the runway. So I loaded it on the runway. The craft shook uncontrollably.... this was undeployed and without wheels. I tried deploying but that solved no problems. I then tried situating it facing upwards rather than facing forward. That also solved nothing. Finally I pushed the transparency button so I could see in the cockpit and the shaking instantly stopped. Switched to Mun base then returned to KSC. The crew was MIA and the rover was sitting on the runway.
So it seems the problem I'm having has something to do with ground contact. And opaque cockpit seems to intensify the shaking. I'm using the latest build of raster prop mon.