Hi, Rosario.
This sounds like you are on the "Simulated APU" until the aircraft begins to move (which disables the simulated Civa APU) and can't establish a connection to the ac's electrical system.

From the Civa manual.

Quote:

In general, simulated APU is available if the aircraft is on the ground and ground speed is ZERO (parked) or NEGATIVE (pushback). In addition a FORWARD ground speed of 0.2 KTS is "tolerated", to overcome a commonly reported situation where the aircraft keeps moving  forward even if throttles are in idle position and parking brake is set. As soon as the first onboard generator is operative and connected to the aircraft electrical system, all installed INS units will automatically switch to generator provided power, and the simulated APU will be shut down. In all conditions, when the CDU BAT light is steady lit, the INS is powered by its own battery.

So the problem might come from the power sources and settings in the C130 not getting recognized by the Civa gauge, so it drops back to its internal battery which soon ends.
I'm not using the Civa in the C-130 but I would suggest to alter the setup of the electrical system, trying to get that battery light of the Civa to stay off. Maybe some special switch setup is needed there.
You can try the infamous Ctrl-E engine start for testing purposes to see if the Civa then "sees" the ac's generators. I think you can press Ctrl-E even after you've manually started the engines. It will just force all FSX internal power settings to "on". This might help.  :)