RX7 won't start without a boost and has newer battery showing 13.6/7 volts. Any ideas?

My son's RX7 will start with a boost and after driving for 5 minutes will start right up after he shuts it off. But after he shuts it off again, it won't start. He thought it was a starter problem and got his rebuilt but the same thing is happening. Battery posts and connections look good. Sounds like a wiring problem but am wondering what other possibilites therecould be