[apalrd]

Only a few seconds?
Not the cRio rebooting (would take like 40 seconds to regain control)
Not the radio rebooting (would take at least a minute and a half)

Could be:
Breakers tripping - Reset would be almost instantaneous for the first few trips because as soon as it trips, the load goes away.
Jaguars resetting - These are really annoying - The Jaguars can fault out for any number of reasons, resulting in loss of that motor for 3 seconds.

If you have a 4-motor drivetrain, loosing one motor could overtax the other and cause it to trip as well. If you have a 2-motor drivetrain, the problem is probably that it is geared too high and the continuous driving current is too much.

The battery voltage has to go down to 5.5 for the cRio to cut outputs. You say it only dropped to ~11 volts while driving? I've seen ours drop as low as 8 volts in normal driving during practice, lower when pushing.

Possible code issues::
If your code takes a long time to execute a cycle, it is possible you are just on the threshold of tripping the watchpuppies. If you trip them, you will loose control, and if you are close to tripping them, driver response will be poor. Look for sources of slow-ness in the thread which handles the drivetrain (such as camera tasks or wait statements). IF it's in teleop, there should be no wait statements or loops.