When the pump turns back on, it should pull air through the venturi automatically... If the tubing gets kinked/plugged, or isn't fulled inserted/sealed in the venturi inlet on the bottom side of the pump, or if the pump itself isn't working as it should, it might not start pulling air again. It almost sounds like the pump isn't pulling like it should to begin with (going back to the recall issues Randy talked about).
How long is the air line going into the venturi port? If it is too long, it might create enough head pressure to reduce the pull of air? Once it's pulling, pour some RO water down the tube (or let it suck it in) and see what kind of reaction you get. That will clear any salt creep that might be building up in the tube (probably already took care of that, but worth a shot), and give you an idea how much it is actually pulling. Check the impellor on the pump, too. Maybe it is cracked/broken. I had a Berlin Turbo that I had to blow start (I know, it's only an expression:D) that I finally realized had a bad impellor. I knew if I typed enough non sense a potentially good idea might come from it. Should I keep going, or will the law of diminishing returns step into play (on something that may have completely diminished before it started:D)?