Just trying to spread the word. If you google Honda Civic Handsfreelink (the Honda Bluetooth brand) you will find no shortage of material pertaining to frequent disconnects and disconnect/reconnect cycling. I ran into this thread on Android Forum which nailed my problem and I thought the more people that know about it the better!
Basically the Handfreelink wants access to the phonebook as well as the phone itself. When it is denied access to the phonebook, it disconnects completely and reconnects to try to get access to the phonebook. There are various "cures" out there which for the most part have you go where no one has gone before on your phone by getting access to the file system, deleting, renaming and otherwise butchering the insides of the phone.
Here is a link to a much more basic cure that worked for me. Since performing the suggested steps, paying particular attention to the part about granting the phonebook access, I have had no problems: