2005 Focus Starting Issues

Good morning all! I have quite an odd issue with my car and was hoping you fine folks could help me narrow down the root cause.

Occasionally, the car won't start. I turn the ignition to start per normal, and it either starts strong or I just get a single 'click' from the engine bay. I've audibly narrowed down the click to the starter. Replaced the starter 3 times. Twice with aftermarket, and the last time with Motorcraft. The battery is new. The couple times it wouldn't start at night I did pay attention to dash lights, radio, headlights, etc and nothing dimmed/went off (except the radio powers off, but that's normal for my HU) when trying to start and the gauges don't become erratic when trying to start either.

Now here's the kicker....during these no start situations, I could try turning the key for hours, but it won't start until I disconnect the battery and reconnect it. As soon as I do that, turn the key and it fires right up. :screwy: Also, it will continue to start without issue for days to weeks (random) after this. So, what you guys think? I'm stuck as to what to look at next and any help is greatly appreciated.