What you are experiencing is a microcontroller brownout due to excessive current draw from the six motors. DC Motors draw the most current when stalled, and six 269 motors can draw over 15A if they all stall at the same time. This far exceeds the current protection in the PIC microcontroller, which causes the power flow to the motors to be interrupted. Heavy current draw can also cause the voltage from the batteries to dip too low and cause the microcontroller to reset, resulting in the twitch-cycle you are seeing.
The workaround is to (1) avoid stalling the motors, or (2) power the motors from a different source than the microcontroller. It sounds like (1) would be difficult to achieve without a significant redesign. You can achieve (2) using a Power Expander and a couple Y cables. You will also need to add a battery for the microprocessor, but since it won’t be providing current to the motors, it will have a much smaller current draw (~100mA). You could probably get by with 9V transistor battery or a 6-pack of AAA or AA batteries.