Is this with the engine running? Also you don't say whether this happens when you turn on the accessories like AC etc.

When you apply the brakes (or any large load particularly with the engine off) there is low going transient on the voltage line due to the brake lights which draw a fair current. With the engine off in my car pressing the brakes will generally cause the empeg to shutdown and restart due to a low voltage. With the engine running there's no problem though. The empeg seems very sensitive to these transients and seems to decide the power is low. Initially it only blanks the screen and turns off the amps so it doesn't actually reboot. It only reboots when the 3.3v supply drops out and the reset chip forces the processor to reboot.

Does it do it when you turn your head lights on? They should cause an even larger transient.

I remember someone talking about a largish (1000uF comes to mind) capacitor connected right near the empeg to filter out these transients. Did a quick search and couldn't find the post - perhaps I made it up.

I'd be checking your power wiring and if possible temporarily wire it straight to the battery terminals.