It's possible the TiVo is restarting overnight, and after booting up, it's taking the 2 or 4 hours (depending on your power-saving settings) of power-up before going back to standby.
There's a way of testing this theory, but it's a little cryptic on a TiVo...
Follow Home > Help & Settings > Settings, and make sure the menu option that's highlighted is something other than the top one. After the box "resumes from standby", go back into this menu and see where the highlight is. It resets to the top-line after a restart.
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