Any idea what's wrong with my car?

It's a 95 mazda 626, manual 4 cyl. , engine just changed and running strong except it turns off every time you start to slow down, press brake or stop. It turns right back on but only stays on when I'm pushing accelerator. Not sure if any of this has anythng to do with it but I was told I need to change distributor cap and rotors. Any ideas other than bring it to a mechanic?