Is the drawing based off a model or hand drawn on the drawing sheet? If it's the latter, I'd say you're missing some relationships. If it's the former, I'd say you have a graphics issue.
The model is used to generate the offset lines (double lines are both offset - original cad is hidden and the dims shown are "driven" from the hidden geometry).
The control q function has no affect on updating the graphics displayed on screen. I end up deleted the geometry and doing it over.
We use these as a rough way to check the profile tolerances of a part and have been doing this for quite some time without have the cad move on its own or unannounced.
The graphics driver does not look to be the latest recommended version.
I've seen this with parts that have driven geometry. I make a change to the assembly, which drives a large change to the part's geometry, which jumps off the page of the drawing.