How old is it?

"My son`s 2001 Mazda .... "

Stuck / defective idle control stepper motor in the throttle body, if it has one ?

General or main dealer workshops are not much good at diagnosing problems - at best they just throw parts at a problem according to the "flow chart" diagnostic manuals provided by the car makers. You could try to find the true fault finding specialist workshop in your area that the other dealers send their "problem" cars to for fixing. I know of one nearby who is exectionally tenacious in tracking down the actual causes of problems, not just throwing parts at the situation hoping to fix it that way. Doesn't charge an arm & a leg either.

Nigel B.