Not to get anyone's hopes up, but I may have found a fix, or at least a workaround.
In the Panda program files folder, there is a subfolder called 'cache'.
I looked at that and thought, 'clearing out caches is often a good idea'.
After first backing it up, of course, I deleted all the files in it.
The program then ran on a reboot, with no crashes.
All the instabilities seemed to have gone away.
The only thing that happened was that Panda started prompting me to OK the running of a lot of program files, so maybe that's where that data was stored before.
After OKing all the prompts, things were still good, but surprisingly the cache folder still didn't seem to have anything in it.
The folder originally contained a .mngr file, a .util file, a .code file, and several sets of .act and .sig files, which were in pairs with the same filename.
The first three files were dated from the date of the program's installation; of the other pairs, one was from back in February, and the others were all from July 3rd this year.
I put all the files back, except the recent ones, which I was suspicious of, and everything is still fine.
So, was there a corrupted file or files in there?