gtmagnet, I've been having a similar issue with bluetooth connectivity being dropped for my Apple wireless keyboard on my mid-2010 iMac. I did what you suggested and Console reported this:
Jul 25 20:38:46 Dales-iMac kernel[0]: [SendHCIRequestFormatted] ### ERROR: [0x0402] (HCI Inquiry Cancel) -- Send request failed (err = 0x0012 (kBluetoothHCIErrorInvalidHCICommandParameters))
Jul 27 16:44:44 Dales-iMac kernel[0]: [AppleBluetoothHIDKeyboard][getExtendedReport] getReport returned error e00002d8
Jul 27 16:44:44 Dales-iMac kernel[0]: [AppleBluetoothHIDKeyboard][getExtendedReport] getReport returned error e00002bc
Jul 27 16:44:44 Dales-iMac kernel[0]: [AppleBluetoothHIDKeyboard][getExtendedReport] getReport returned error e00002bc
Jul 27 16:45:06 Dales-iMac kernel[0]: [SendHCIRequestFormatted] ### ERROR: [0x0406] (Disconnect) -- Send request failed (err = 0x0010 (kBluetoothHCIErrorHostTimeout))
Jul 27 16:45:06 Dales-iMac kernel[0]: ### ERROR: send request failed (err=10)
Any idea what these particular error codes pertain to or where I might find the answer? Thanks in advance!