01 Yukon wont stay broke long enough to fix

[86 Silverado LS1]

Guys I need some help. I can’t figure this one out. 2001 Yukon 5.3 70,000 miles. We have owned it since 2002. You try to crank it up and no start. None at all. Like it is out of gas or has no spark. It has done this about 5 times over the last year. I have seen no pattern to it whatsoever. It is usually after a short trip and rest like a trip to the grocery store. You come out of the store and no start. The bad part is it wont stay broke long enough to find the trouble. It will always start back up after some time???
My first thoughts were fuel pump. I figured it was getting hot and when you cut it off it would not pump until it cools. So I change out the pump and the connectors for the pump. That didn’t fix it. Now I keep a fuel pressure gauge in the truck in case I can get it on there when it won’t start. Well, last night it happened again. We came out of the restaurant and no start. I put the gauge on the fuel rail and it has a good 60 psi. So I start thinking about spark. Could it be the factory security system?? I did notice the security light in the dash on last night. Anyway we were using her keys in the ignition but we unlocked it with mine. So just to try it, I took her keys out and tried mine and IT CRANKS!! Can the keys even have anything to do with it? What about locking it with the remote then unlock with the key? Can any combination of this trigger anything with the factory security system? Does the factory security system have the ability to keep the motor from starting? The security light in the dash seems to have a mind of its own. I don’t know what triggers it but it does come of from time to time.
The truck does have a remote start. Can that play into this? I had it installed using the factory remote. You have to hit the lock button twice for it to crank. I guess it works off the old blow horn to verify lock thing. I don’t think this has anything to do with it but I’m not sure. This is the wife’s ride with the baby seats in it so you can see how this is a problem. Any ideas???

P.S. I know this isn’t a LS1 but I’m not exactly a member of any Yukon forums.