You didn't say which battery you were running, but I'm assuming the factory battery. Since the camera powers up on AC, the problem could be either a battery problem, charger problem or (most likely) the onboard battery/AC switch built into the power socket. This switch seems to be fragile, and seems to fail (get stuck) in the AC mode, which makes the camera think the AC cord is plugged in when its not, disconnecting the battery socket. If this is whats going on your looking at a JVC service center visit.
If you still use factory style batteries, you need to ditch them and get a professional battery, it will make a world of difference, and eliminate the power socket switch problem, and all the other battery headaches
If you plan on keeping the camera for a while, now is the time to change over while you can still get battery mounts from JVC.
I like (and use) the Anton Bauer Tandem Charger, and the Trim Pack 14 Logic Series battery. This battery will last for a couple of hours under normal use. The nice feature of the tandem charger is that it acts as the AC supply, and mounts to the camera like the battery. The tandem can be mounted on the camera with the battery, so you can charge while shooting on AC. If you pull the AC, the charger passes the battery power through to the camera without interruption. The AC cord is a standard NEMA, which is a lot better than the fragile factory charger/AC system. It also conditions the battery, like most AB charging systems. It is a very flexible set up.
The downside is the battery will make the camera back heavy (which I actually like), and the cost. Charger, mount and one battery will set you back about a grand. Additional batteries are about 200 bucks. If you want to charge multiple batteries at the same time, you will have to spring for a different charger.
IDX also makes a set-up for this camera, same basic price range. I went with Anton Bauer because I like the AB-JVC battery mount better, and I have used AB products for years and they have always worked well.
Thank you very much for the advice. Makes sense, I was just hoping to avoid the extra expense since 99.9 percent of my shooting comes with AC, so I elected to use the factory-type batteries as a cost vs. use deal.
I greatly appreciate you going to the trouble to respond.