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I had a similar issue on a vehicle doing the same thing and it ended up being a harness wire grounding out next to the alternator. Had another one be the alternator itself. What it was doing was backfeeding through the voltage regulator in the alternator and is was powering the relay with the backfeed causing the clicking under the dash. I would have the alternator checked for you might have one going bad and causing this. It will cause a no start for it will open the loop back to the battery from the PCM feed.
Next which is common is the solenoid for the ignition. See if the one by the battery is acting up followed by the starter solenoid on the starter itself. They can both cause intermittent issues like you are having.
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