My 90 Z51 used to shut off all the time when I hit big bumps- turned out to be a power distribution block behind the battery.
Frankly, it was the worst car I've owned. Bought it with 19K on the odo and sold it with 86K on the odo. Constant electrical problems and it was generally a pig to drive. 6 speed car on original clutch but it was getting tired.
I'm lookin at a c6 z06 when the price gets around $30 for a good one