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You don't mention ANY details on your Z, including mileage, mods or any past trouble that might provide a clue. But this is not a known problem that plagues the Z33 and you may have trouble codes in memory that'll help to diagnose the problem(s).
Start wire and mod tracing. Bet there is a wire or mod touching and grounding on something.
^ this. Also make sure all the electrical bits (fuse boxes, junction boxes, ECU and bcm) are properly secured. Something is likely loose and flopping about.
Would like to know any mods? Electrical? Anything at all. Let us know and we can help! Sounds like a connection short circuiting, or grounding out in the wrong place!