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