What causes the cqr to not start at random times but after resting a few minutes it will start?

Ignitionswitch on steerin colum or the keylock. Nevr go to a dealr..bad techs n doublprice

99% of the time if ALL power is lost then comes back it's dirty battery cables.

Many possible causes - have you looked for trouble codes (DTCs) with a code reader?

Install a new crank shaft sensor. I had the same problem with my wife's Jeep. It would run fine fore days at a time then quit. When the crank sensor goes out their is no spark or injection of fuel into the engine. This is a Hall Sensor. They can be intermittent, and affected bu heat. If your Jeep will not start, try freeing the sensor and see if it starts. Cold Freeze is used in electronics to test

i would check the cables on the battery first could be loose also look at the engine side of the cable use jumper cables to jump the cables one at a time to see if the cable is bad

It could be a loose battery cable to starter connection or loose ground wire or corrosion on the battery cables or wires. I would check all connections and wires for looseness, wear and corrosion and tighten or replace as needed,

THE SWITCH IN THE STEERING WHEEL IS PROBABLY GOING BAD OR HAS A LOOSE CONNECTION THAT IS GROUNDING OUT AND COMPLETETING THE CIRCUIT AT RANDOM. I REALLY DONT KNOW HOW OR WHY SHUTTING IT OFF WOULD TEPORARILY FIX THE PROBLEM BUT WITH ELECTRICAL PROBLEMS ANYTHING IS POSSIBLE BELIEVE ME. ALSO TAKE A LOOK AT THE WIRING AND THE HORN ITSELF TO SEE IF EVERYTHING LOOKS OK THERE.

check to be sure you are getting a good connection on your battery terminals.next check the hot wire from your battery to your starter .if all of this is alright .the problem is most likely your starter.the contacts in the starter solenoid will cause the this clicking sound.the contacts and contact piston are replaceable and some times you can clean them with a file and emery cloth and put it back together and may be just fine.but that just depends on what kind of condition they are in.

I'd rechagre your battery fully then test the alternator. It sound to me like you have a bad alternator.

May not be 'loose' wiring but you are headed in the right direction if you haven't already found the problem.

This is a common problem and is almost always caused by battery-related cables.

You will need to remove both cables at the battery and clean them with a $3 tool that will do both the female and male clamp parts.
You should also remove and clean the positive cable from the starter itself.
Since you are already dirty, take the extra five minutes and remove and clean the point at which the negative battery cable is connected to the chassis.
At each of these points, thoroughly protect the cleaned connections with at least a glob of petroleum jelly or (if you are at an auto parts store anyhow) 'dielectric' grease. Either of these will delay the next cleaning cycle by years.

ALWAYS remove the negative (ground) cable FIRST.

The bad connection is dropping ALL of the 12 volts when trying to start since the starter draws 100+ amperes and any cruddy connection is enough to drag down (drop) the voltage so far down that all devices that depend on getting at least 9-10 volts will reset themselves.
After the engine is running, a bad connection becomes less important since the other items being serviced don't draw anywhere like that amount of current and the alternator can operate these and still charge the battery regardless of the bad junction.