I have noticed similar behavior on number of occasions. I have an exchange account configured as well as gmail. I've tinkered with both accounts when the activity icon remains active and narrowed the problem down to the exchange account that is set to push with sync active on mail, contacts, and calendar. There is never any mail waiting to be received or sent when this happens but I access the exchange account from multiple devices throughout any given day so keeping the iPad in sync is required. I suspect the additional overhead is the sync task running in the background. The activity icon does eventually return to idle status (no longer displays) after a few moments. I also noticed if I turn off sync on the contact and calendar this also ends the additional activity being observed.