Hmmm...

How long does it take for the lockup to occur? Minutes? Hours? If minutes, I would think it software (hijack spinning down the drives, application conflict, player starved, etc.). Hours implies heat, software (memory / disk handling).

One thing to try would be to take the top cover plate off the player. This would allow for greater air flow and convection cooling. See if that helps.

Do you see this during regular use, or only when trying to backup the player like this?