The same here
I got the same problem. Got newest not rooted, stock Xperia Tablet Z (sgp321, android 3.2.2). Im using it with motorolla bluetooth keyboard + logitech bluetooth mouse v470. With mouse there is no problem it stays connected all the time. But keyboard disconnects & reconnects randomly. Some times its 10 sec & somtimes its more then 3 minutes. It happens even during text input so i loose some chars during text input.
I`m using external keyboad helper app to remap my national chars, but I`ve tested that it`s not connected to the problem.
I`ve noticed that when i connect bt keyboard, in the system input settings Xperia shows Hardware keyboard and I think it is bad implemented function. Choosing option to disable HW keyboard during connection some times helps me to avoid reconnect problem, but its steel not stable.
Maybe this ideas can help to solve the problem....