Check the FAQs, we get similar questions a lot. Scotty has lots of videos diagnosing this kind of problem. 

https://carkiller.com/scottykilmer/qa/nostart/

Assuming you've already tried replacing the starter relay and examined its fuse, and you're still not hearing (or feeling with your finger) the starter relay clicking when the key is turned to START, it seems like the problem is on the Control Side of the Starter Relay circuit.

If you pull out the Starter Relay, its junction box terminals are configured like this:

Starter Relay socket 3 gets power from the 30 amp (F13) starter relay fuse.

Starter Relay socket 5 goes to the "S" terminal on the starter solenoid.

Since this is an intermittent problem maybe carry a 2 inch piece of wire in the truck.

The next "No Crank", leave the Key in ON/RUN, (make sure you're in Park so you don't run yourself over), and use the wire to jump sockets 3 and 5.

If the starter turns (the truck will start), you've pretty much confirmed the problem is on the Control Side of the Starter Relay circuit.

Starter Relay terminal 1 gets 12 volts to provide power to the starter relay's coil when the key is in START AND the truck is in either Park or Neutral.

Starter Relay terminal 2 gets a Ground from the PCM to energize the starter relay's coil (which closes the relay contact to connect power from socket 3 to socket 5 and turn the starter).

You didn't say if you're comfortable using tools like a multimeter.

If you are, during the next NO CRANK, have somebody turn the key to START as you use the multimeter to check for Battery Voltage (10.5 to 12.5 volts during cranking) on Starter Relay socket 1.

Frankly I'd be surprised if it's there.

Your 2013 Raptor has a component called a "Molded Lead Frame" inside the transmission. it's bolted to the valve body.

It's Ford's redesign of the external transmission range sensor that worked perfectly fine and didn't need redesigning.

It looks like this:

You don't have to pull the transmission to replace it but you have to drop the valve body.

If you find that this is a control side issue on the Power side of the starter relay, this is a component which would be a suspect.

Another thing, I pointed to the output speed sensor that's mounted to that component because there was a recall concerning that.

It seems the voltage signal from it dropped out and the computer assumed the truck was in 1st gear. People would be cruising down the highway at 55 mph and the truck would downshift to 1st and lock up the back wheels.

Check your VIN to see if that recall applies to yours

get someone to tap the starter while you turn the key