Honda Element / Cuts out to dead stop

I have a 2007 Honda Element. It “cuts out” randomly. From driving - to a dead stop. After stopping, it acts as though it has a dead battery (barely cranks) though the accessories continue to work. The first time I was on a hill in very cold weather, at night. Had it towed to my trusted mechanic. It started the next day. I then took it to Honda. They found a short in the ignition switch. This made sense so I had it replaced. The next time it happened in a major intersection while towing a boat. After 5 or six tries it started. Took it back to Honda, they could not pinpoint the issue.

At this point I consider the car dangerous and (because I have morals) worthless as a trade in, as I would not trade without revealing the issue.

This has happened once or twice in a more minor way, the car just cut out briefly without out
stalling.

When it cuts out - do you mean the engine stops? And when you try to restart it, does the starter motor crank the engine, but the engine fails to start and run? Or is there no sound of the starter motor turning the engine? Or does it barely crank - turns much slower than usual - every time you try to restart?

The engine stops. The engine cranks as if the battery is dying. after 5 or 6 tries it starts.