[Al Skierkiewicz]

Everett,
It is likely that the power supply in the amp is unhappy. This power supply appears to be a switching supply and can have some pretty high starting current demands. First off, the battery needs to be near the power amp and the cables should be #6 the same as the primary wiring for the robot. (The manufacturer recommends #8 minimum.) The power cables should also be very short, just like the robot. If you are using long or small gauge cables, there is too much voltage drop in the wiring. Large capacitors may help with sudden low frequency demands on the amplifier. The caps listed in the accessories section should be OK but you are spending a lot of money on the LCDs and lights. If you use one, mount the cap very close to the power input on the amp. The amplfier should be turned on with the volume very low as well.
The specifications for the amp in the Crutchfield link says it is intended for 14.4 volt input or the voltage normal car systems might have during battery charge. The manufacturer specs the system at 14.4 volts for distortion and power output. Our batteries are lower at 12 volts nominal but lower dependent on load.
You didn't mention whether you are running the amp in the mono bridged mode or standard stereo. It is unlikely you will need the full power of the bridged mode on a robot cart but the speaker should handle it depending on the enclosure. If you are running in bridged have you followed all the instructions for wiring? I ask because bridged amplifiers cannot have the output tied to battery common. i.e. the output to speaker wiring is different than in standard stereo mode.