Bad ignition switch?
 

I'm trying to figure out why my car shuts off from time to time. Always while driving, sometimes on the highway.

What happens is it'll shut off and turning the key won't engage the starter and popping the clutch while in gear won't start it either. Usually have to let it sit for 10 or 15 mins, then crank it and it starts right up.

I've checked the battery, starter connections, grounds and I replaced the main relay.
Could a bad ignition switch cause this issue?

Do you have a starter cut relay? If the car shuts off you want to test the Black wire at the ignition switch for constant voltage as it should always be present. If it is present then you want to check the voltage on the Black/White wire at the Main relay's two wire plug. All of this would be done with leaving the key in the position it is in when the car kills itself (which should be the on position). If there is no voltage at the ignition switches' Black wire then that is the cause.

Is it possible for a bad ignition switch to be able to turn the starter, yet not allow ignition-keep it from actually firing/starting?

When you turn the key to start the Black/White wire of the switch also receives power. This wire powers the main relay which powers the ECU. If this wire has power w/key to start and the starter is turning over then the switch is doing its job.

I asked the q about a bad switch keeping it from firing even though it allows the starter to turn because the reason I let it sit for 15 or more minutes is because the starter would eventually turn, but still no start. Seems after 15 or so minutes, then it would start up as normal(dunno how possibly heat cld affect the ignition switch)

That being said, I drove all the way to and from work yest with the new switch and no problems yet--so I'm hoping that fixed it.

Could be. Had an ignition switch on a Ford where the plastic pins (on the electrical portion) weren't moving freely. I heard the grease was thickening enough and there was a TSB on them.
If it doesn't end up being the ignition switch, I'd check relays.

No problems for close to a week after replacing that ignition switch, then it happened again on the way to work this morning. Doin around 65/70 in the fast lane, hit a bump and the car shuts off. While coasting to find a good place to pull over, I turned the ignition off, then put it in the on position, dropped it into 4th and tried popping the clutch a couple of times-wouldn't fire. Pulled off onto the shoulder, tried to start it, the engine cranks but won't start. Let it sit for 10 minutes, cranked it-starts right up.
New new main relay, new ignition switch-so I've gotta assume the problem doesn't lie there.
Any ideas?

Check the fuse box under the hood.

When I first bought my car, the headlight retractors didn't work, had to fix the stupid fuse box.

You need to perform some diagnostics after it occurs and this means leaving the key alone. There's a 4 wire Green check connector near the lead coil which has a Black/White wire and if the car dies, and you just leave the key alone (on position), then the B/W wire should have voltage and if not then you have greatly narrowed down the problem. Also, the Black/Yellow wire at either of the coils should also have 12 volts. If they both have voltage then check the Brown/White wire of the pressure sensor as it should have 5 volts. And you could have a ground problem related to the ECU.

Had a similar problem when my RX7 was new (I am the original owner of a 90 GXL). The car would cutoff while driving. I would pull off to side of road, let car sit 10-15 and it would start right up. Turns out that it was the AFM. Actually, I believe that it was a resistor in the AFM. The problem was intermittent so it was hard to diagnose. Have you tried pulling trouble codes?