Bluetooth peripherals randomly disconnecting under Mavericks
I was able to overcome the problem with this quick fix. So whenever you loose bluetooth connectivity just run the following commands in the terminal

$ sudo kextunload -b com.apple.iokit.BroadcomBluetoothHostControllerUSBTransport
$ sudo kextload -b com.apple.iokit.BroadcomBluetoothHostControllerUSBTransport


You will regain connectivity.