The air pressure setting has to be 1-2 psi less than your 30 psi cut-in or the tank empties before the switch calls for the pump to come on. If not, that makes the water stop flowing before the pump comes on. You set the air pressure with no water in the tank. Try tighetening the tall screw's nut a full turn, that increases the cut in and out settings and will get the switch above the 31 lbs of air pressure. In other words rasie the cut in setting. Thta's instead of removing air from the tank.
Another cause is a blocked switch nipple. If it is blocked with rust/dirt, the switch lags in seeing the pressure change and causes the pump to come on and shut off after it actually should.
Quality Water Associates