The Ps3 (or P30) air line is a primary means of determining the limits to fuel flow (max & min) that the engine can instantaneously tolerate. The fuel flow must stay between these limits: Too much fuel, and a surge or overtemp may occur; and too little flow, a lean blowout (flameout) is likely.
Thus you can see a blocked air line causes the control to think the engine is at a lower-than-actual setting, and may thus deliver less fuel than the engine needs to stay alive.
Think of it as maintaining the fuel/air ratio within safe bounds.
