I also experienced this randomly with the standalone at times. With my game, the stock uzi-soldier character would be visible for about the first three levels, and then from the fourth level (quite a big level) and up, the uzi-soldier would become invisible.
Okay, so I experimented first with hand-copying over the uz-soldier files, did not solve the problem. Then I remembered that I had standalonefreememorybetweenlevels=1 in my setup file. I changed that to standalonefreememorybetweenlevels=0, and after testing it for a while, it seemed to fix the problem, so far.
Dunno if this is what caused the problem, further tests may be needed. Maybe the good GG peeps could also check into this.