I also have this problem with my desktop. It does seem to have started sometime after the update. My issue it is that the Bluetooth connection drops after waking up from sleep mode.
I just got of the phone with an Apple Representative. He had me go though some kind of Bluetooth reset by restarting and holding down four keys. It worked for about a minute, until we hung up the phone, and then it was back to "Bluetooth Unavailable" again. Before he hung up, he sounded very unsure that this procedure would really work. He mentioned a deeper sort of reset, or whatever, which might be necessary if this did not work.
It is a real bummer having to restart the computer all the time to recover the Bluetooth connection.
For me, this whole thing started with the mouse not working after waking up from sleep. The after fiddling around for a while eventually the mouse would reconnect. Then it was the mouse and keyboard losing connection, and then again eventually restoring their connection. Then it became a dropping of the Bluetooth entirely, stating "Bluetooth Unavailable". I went through the fix that involves removing plists. That did not last. Restarting fixes the situation temporarily, but the connection usually drops again even without waking from sleep mode.
It is disappointing that Apple seems to be ignoring these Bluetooth Connection drops comments. This seems to be a big problem for a lot of people, with the question just being asked in different ways. I figure they must be working on it, but it would be nice to hear from them.