My daughter has a Keurig and has run across this problem from time to time. She does the same as you - pulling the tank off and replacing it. Sometimes she raps it gently on the countertop to dislodge any bubbles in the intake.
I know from owning a couple of high end espresso machines with water tanks that it's usually caused by air bubbles in the feed tube or intake valve. This makes the machine's sensors think there's no water in it, and that the circuit needs to be primed (and priming one of these bad boys isn't always a quick or easy thing to do). It can be triggered simply by filling the reservoir too quickly from the tap and creating a lot of aeration in the water.
We've solved the problem in our espresso machines by using only distilled water, which contains very little dissolved oxygen. Distilled water also has the advantage of virtually eliminating scale buildup.
If that's not an option, you might try what this guy recommends: