Although caution should be advised since the is a sample size of 1, I left the Juice Pack Air on my 3GS on charge all of the time. It seemed to have no ill-effects after 1.5 years. My hope was that it would protect the battery so that my kid would get a few years of using my 3GS as a hand-me-down phone.
Mophie do claim that leaving the switch on charge all the time wastes a little power (charging always costs power even if the main iPhone battery is full). However, it is not clear whether leaving the charge on all the time protects the battery as I have supposed or whether it might harm it. In any case, even with the JPA set for charging all the time, I do cycle the battery on our iPhones periodically as per Apple's guidance.