I'm having the same issue. I purchased the compact charging dock, which comes with their rechargeable batteries, and I've had nothing but issues with them. It will stop working during a gaming session, and I have to open the cover, pull it down from the connector, so that it powers the controller back up.
The batteries are charged correctly as they report 100% power when playing.
When the Meta supplied batteries are fully charged they cause the random disconnect problem. After 15 or 20 minutes of play when the batteries have drawn down a bit they seem to stop disconnecting. At least in my experience.
No. There is a spring-loaded contact in the controller +ve side that can get jammed and the battery becomes a bit loose. Use a bit of aluminium foil like I suggested earlier.
