Car silencer back fires and the car stops

Dear Sir,

I have a mazda 3 2007 model , 1.6 liter engine, it is backfiring and stopping suddenly, and will run fine after some time for a while and again the same problem comes back, i did the following
1. changed gear oil
2. Changed plugs
3.Changed fuel fllter.

Still the problem doesnt go, and the mechanics dont have any clue.

Please please help me in this regard.

Thanks and best regards.