Car losing power on turning key, but returns shortly after

The battery is probably dying. But in a way that at some times it behaves like it's completely dead and then it works fine.

It happened to me. At one point it died and never came back. I thought that there's an electrical problem with the car because batteries usually don't suddenly go from perfectly normal to empty.

Put a voltmeter in your car. Next time it happens measure the voltage directly on the battery. If it shows anything less than 12V the battery is the problem, replace it.

I would look for a ground problem. Check your battery terminals and clean them. The fact that it happen intermittently suggest a loose connection. next time it is happening, before turning on the key, turn on everything you can. headlight on high. brake lights, see if it fails. also try turning key on/off a few time, might be the ignition switch failing, bad contacts. But I doubt that, cars too new. when you turn the key on there is much more of a draw on the battery, a bad connection will fail under a moderate / high load. but will work with a little load. the radio resetting is a symptom of this.