Why does my grill have a small flame even though there's still propane in the tank?

Every now and then my grill will act like it's almost out of fuel (low flame, etc) even though the propane tank still has plenty of gas in it. If I lift the tank I can feel gas sloshing around inside, and it's still heavy. The last time it did it I disconnected the tank, checked all the hoses, reconnected it and it seemed to work again, but the grill is less than a year old and is in very good shape. I've also had the same problem on my previous grill. When I get new propane, I swap the tank, so I've had the same problem with different tanks and different grills. This time I was able to get it to work again, but previously I've had to swap half-full tanks. When I swap the tank it always works again. What gives?