Apparently I am no genius either (ok, no rolling of eyes!) because a friend came up with a solution that I should have thought of myself. After talking with Pentax Support, who were scratching their heads too and wanted me to send the camera in, a friend called and he made a suggestion. Clean the battery terminals and camera terminals. By eye, they both looked clean (new camera after all). But after a few swipes with a q-tip and alcohol, I put the battery in, let it set for 10 minutes then went and pulled the battery out. After 30 minutes of no battery it is still remembering the time. Camera was getting power before, but maybe something was going on with the terminals. Either way, the solution was simply: clean the terminals.