sounds like the immobilizer is not un-arming therefore the car is still being immobilized! I would think it caused when it happens by a bad connection! - These can be a complete pain in the rear end to get fixed, even by a good auto electrician as sometimes the fault is not there so you can not find it to fix it! I am dealing with a prob like this on my toy at the moment too!!!

 

I had a starter motor do the above.
Sometimes it was fine, other times nothing.
I replaced it in the end and all was fine.
Worth checking all your connections, earths etc.

 

Check the ignition switch as well. Common for the wire connections to fail.