It takes a big voltage drop to cause a reboot - down to about 10V I would expect a power warning symbol, screen blank, then resume without reboot. I think you would be dropping under 8V to get an instant reboot - or, perhaps, the problem is actually a spike caused by the main beam relay.

If your amp is really drawing up to 140A you should definitely have a big cap on there - 1F or so. A small cap on the 12V line might solve your reboot problem, but I would investigate the cause of the problem before doing that.

Rob