My 2001 Mazda MPV is stalling and has a rough Idle. While driving the van the vehicle stop runing, After letting the vehicle sit for a while, the vehicle will start. This has happened a couple times over the last months.

Might be the Brake Booster do you have a CEL coming on?

Have you cleaned the throttle body bore and plate of any black carbon ? The idle air control circuit may be clogged or the IAC may be stuck closed .

looks like not enough fuel pressure, check the fuel filter.
and the fuel pump pressure.with car running 60 psi
the pump is located at the rear seat driver side you have to remove the carpet to access the cover. if the fuel pressure checked "OK" suspect defective maf sensor (sometimes defective maf sensor do not show errors codes)another way to test is disconecting the maf sensor and start the car (computer goes to limp in mode) and works little better,or check by scanner idle= low grams per seconds and increase when accelerate.

Check your fuel vapor recovery system, your van has unusual set up, and the effect is RAW fuel gets purged, rather than vapor.
The dead giveaway test is does the issue happen on light acceleration? Does it stop if you let off the throttle? Can you accelerate harder and "get past" the issue?

than I would have the fuel pressure check and change the fuel filter

I ahve same issue with my 2004 MPV. I replaced the plugs, coils etc. No help.

did you ever get it fixed?

This sounds like a classic case of either a dirty/faulty IAC (Idle Air Control) motor or a sticking EGR valve. If you can prevent it from stalling by keeping your fot on the gas slightly and it always restarts right away and runs good when restarted, I'd suspect the IAC first. If it "chugs"when stopping and will run rough even with a little (not a lot) of gas pedal and/or it runs rough when restarted, I'd suspect the EGR.

check the key switck if it stop when you move it from start to run. bobg22

On my MPV the problem was actually the Switch not the motor. Check the switches. You can access them by just pulling the door panel off. If you need some instructions for door panel removal let us know.

Hope this helps...

If it's the gas, it would run rough on all cylynders.
try putting fuel system cleaner (redX) or the like and see if it may be a blocked fuel injecter or jet( this may also clean the O2 sensors.