I wish I knew of a way to make this problem go away completely, but the best I can give you is a workaround:
1) in the bluetooth menu hit the "X" button to remove G613 from the list of connected devices
2) hit the connect to "bluetooth" button on the keyboard again to make G613 discoverable.
3) when the keyboard shows up in the bluetooth menu hit "Connect" and punch in the PIN as asked
4) You're back in business until the next connection interrupt :( Rinse and repeat.
This, along with the useless and annoying macro keys, really makes me wish I went with something else for my wireless keyboard.