The air-diff, or as I call, dog feces, is prone to problems. This is one of them, and unfortunately, I think the frequency of problems like yours will increase over time. First, I saw pumps just seizing up in the early years of this platform. Then lines began to age, crack then leak. Then seals and other internals begin to leak, and the little air pump can't keep up with more than the tiniest leak.
If it's the acutator, you got to choices.
Good: rebuild it with new or used parts (I think I got a box of these parts *somewhere* if you really need). Prolly best bet for you if you like shift-on-the-fly without having to lock your hubs, of if your having a shop do the work.
Better: Do the air diff elimination. While not easy or for the faint of heart, it puts the front axle back to they way it was under the Sidekick platform, and opens up gearing and locker applications if thats your thing. No one has flashing 4x4 lights in a Sidekick unless the shift lever isn't fully engaged.