I've had my Zen V Plus for a few days now and have figured out one charging problem --
You cannot leave it plugged in overnight to charge. Here's my take on it -- It will not let you turn it "off" while plugged into a charger. If you turn it off, it comes back on. I believe that it charges the battery for the first few hours until the batter is fully charged. Then the charging circuit cuts off, but the player stays on. It sits there the rest of the night in the "on" state, draining the battery with the charging circuit off. When you "wake" it back up in the morning, the battery is nearly drained back down to nothing.
I think you have to charge it, unplug it, and then power it down.