[Al Skierkiewicz]

The 78XX series of regulators need at least two volts across the device to meet regulation spec. That is why the RC drops out below 8 volts, it also has a 7805 internal. (BTW that is why the current in the RC is limited to 1.5 amps, the max current spec on a 7805) When the input falls below the required 2 volt differential the output falls at the same amount. This is a problem that gets power supply designers into trouble all the time. If the input ripple from an AC simple linear power supply (wall wart) falls below the 7 volt minimum, then the output of the 7805 suddenly has ripple.
The 7.2 volts battery may measure at 8.4 volts when it is charging or slightly after. It is generally at 7.2 volts, or 1.2 volts x 6 cells for NiCad battery chemistry.