It may be the fuel pump relay failing intermittently. The next time the car will not start, try to listen near the fuel tank for it to prime when the key is in the, "ON" position. The fuel pump comes on for a second or two to prime the fuel system when the key goes to the, "ON" position just before starting it. So, if the relay, or maybe even the pump, is starting to fail intermittently, you will not hear it prime when the key is in the, "ON" position. Of course to see the difference, try doing this when the car is running without issue and listen for the, "whirring" noise that the fuel pump makes when priming.
You can also have the trouble codes pulled by an Advance or Auto Zone parts store for free. This will help a lot to diagnose the problem.
When you get the outcome, let me know and I will reply ASAP.