I did some testing tonight and determined that if you toggle the battery switch twice your CIVA power will not fail.

Powering the aircraft or the CIVA unit first doesn't appear to make a difference...just have to toggle the battery switch!

If you start with running engines then this 'fix' doesn't do anything, only in a cold-n-dark state.

Edit: This doesn't work from a saved cold-n-dark flight. It will work from starting with the default aircraft, shutting down the fuel (Ctrl+Shift+F1) and the battery (Shift+M) then load the 727.