I have a 2001 Mazda 626 with a v-6 manual transmission. When you start the car it will go dead unless you rev up the engine. If you two foot with the clutch and gas you can drive all day but when you go to stop at a light or turn and the idle goes down it dies immediately. It starts right back up as long as you push the gas.
From your description it sounds like you have a sticking idle air control valve. When they stick you will need to hold your foot on the gas to keep the engine running. You can try to tap on the valve to see if that will free it up.