What about your VATS chip possibly being bad in your key? Have you switched keys and tried this when it happens?
Does it crank but just not start or is it completely quiet when it happens?

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1998 Six Speed, Torch Red Coupe - K&N CAI, Vararam Velocity Stack, Z06 exhaust, Z06 sway bars, Z06 intake, C6 Z06 shifter, stainless steel brake lines, Z06 shocks, Borla X pipe, drilled/slotted rotors. Dyno'ed at 330 RWHP & 340 RWTQ.