I'm having the same problem. Someone on another forum suggested deleting the pairing profile on the PlayBook and keyboard, and going through the reconnection process again. This has resulted in the PlayBook-keyboard connection staying on for longer, but it seems every couple of minutes or so, it cuts out and I have to turn the keyboard on and off to re-establish the connection.
Other advice has included holding down the blue "sym" key to reconnect. However, aside from being a nuisance, it doesn't work for me. My next resort will be to email support, which is apparently minikeyboardsupport@rim.com.
