I am having similar problems and have been talking to Apple support today.
I have a Jawbone Icon and iPhone 3GS. The headset constantly disconnects and reconnects meaning that leaving the unit in your ear is impossible. When a call comes in more often than not the signal has been dropped and the call will not route to the headset.
Having contacted Jawbone, they replaced the headset but the problems were not resolved.
Having called Apple 3 times each agent responded differently. I have now tried resetting network settings, resetting the phone and factory restore. On the third call the agent said they couldn't help or troubleshoot at all because it is not an Apple device and to try an Apple headset which is no longer available.
However, to add another twist, the Apple store recommends the Jawbone Icon for all iPhone generations (
http://store.apple.com/ie/product/H0495B/A?mco=MTY3ODQ5OTY).
I have also tried the Icon with two other phones (not iPhones) and 2 other headsets with the iPhone. The Icon works fine with other phones and the other headsets have the same issue with the iPhone.
So it seems an obvious iPhone problem to which end Apple are not willing to help resolve.