I recently bought a P reg 1.3 Encore. The last 2 days it has been cutting out as I brake to stop at junction/etc. This has only happened once in the dark and all the driving lights went off. Still had dashboard display.
I had this problem once in an Audi I had..it turned out to be a faulty Cold Start Valve in the Fuel injection distributor head unit. I don't know if you have Fuel Injection in the Fiesta, but if you do, then it may be worth considering..
I have a p-reg fiesta encore and the same thing happened to me.It turned out to be a split hose.Theres a hose that runs from the rocker cover just left of the oil cap.the hose joins a 4 way adaptor.It cost me a tenner from arnold clarkes for the 4 hoses. hope this helps