I would suspect the coin cell for the real time clock as you mentioned. Especially if it's an older camera, it could indicate the battery is low and needs to be replaced. Also if it never did this before and only recently has been doing this, it's likely the battery. 

I think this is a known problem with some Bushnell models. The battery connection only needs to be interrupted for an instant (by being moved for example) and the camera resets. If a coin battery, are they still charged?

I am having similar problems with a campark camera. It's more than 4 years old, so it could be the button cell. I am also suspecting that humidity plays a role : the re-set happened a couple of times after long rain periods ( half a day or so ). Perhaps it was coincidence, perhaps some corrosion is going on.