Check your starter relay. I had this exact same issue. The car would start fine sometimes and would randomly not start. I would hear an audible click and after a battery, a starter, and tons of swearing later, I swapped out the relay. Voila, haven't had the issue since. The greatest part was the starter change took nearly 10 hours thanks to a rounded off head on the upper bolt. Gotta love POs attempts at fixing things... Good Luck!
-Matt