[Al Skierkiewicz]

Dale,
So we all get on the same page here...
Only four CIMs are allowed on the robot. CIM stall is 133 amps. Battery can supply 500 amps for a few seconds, although I would guess closer to 600 on newer batteries. (also the spec on MK batteries is 750 amps) Battery internal impedance is 11 mohms (.011 ohms), #6 is .0005 ohms per foot. Figure the same loss the Anderson connector, main breaker, and terminals on the battery and PD and you are likely pretty accurate on the total losses. I would guess that .015-.02 ohms would be pretty close.
The battery connection on the analog breakout in Crio slot 1 monitors battery voltage and inhibits Crio output when the supply voltage falls below 5.5 volts. The internal power supplies on the PD (+24, +12, and +5) drop out around 4.5 volts. If the voltage droop is sufficiently low and sustained, the Crio and radio are likely to reboot. The Crio will take about 30 seconds or more (typical) while the radio takes 52 seconds minimum. The power supplies are independent. The Crio is speced to work down to 19 volts and the +24 volt load will affect this power. This includes +24 volt solenoid valves and sensors. Please remember that battery temperature also affects the amount of available current as well as internal impedance.
While a second battery would help, most teams do not need it and play fine without brownouts.

Jared, after watching the videos I believe the Crio and in one case the radio as well are rebooting. I commented in my reply but if you would like to tell here what drive train you are using, I can reply here as well.
AL