I remember reading about the higher modes causing problems on the AGA chips due to more heat they create. Putting some heatsinks on the AGA chips might help with the issue. Before IndivisionAGA these modes were unuseable.
That makes good sense. As the chips heat up, or overheat, the image begins to degrade. If this is the cause then a reboot would only clear the problem for a shorter period of time, as it would take less time to have the chips overheat again, if it took any time at all. A cold boot would be more effective and last longer, depending on how long the Amiga was allowed to cool down.
With this in mind, it should be fairly easy to confirm that the problem is being caused by heating up of the AGA chips, and fairly easy to resolve with heatsinks and/or better cooling by use of a fan. I'll have to do some testing when I get a chance.
Edit: If the problem is due to overheating of the Lisa chip that the Indivision is clipped on top of, that may be hard to cool off and resolve the problem.