how can i stop my car from cutting out in low gear?

my 1994 nissan micra has started to hesitate when driving at normal speeds and the engine cuts out intermittantly when I slow down at roundabouts or turnings. The mileage is approximately 59k. I am aware that there is a small hole at front that allows water running from windscreen drainage channel to leak into the passenger foot well. Can this affect the electrics? Took it to the garage but the problem didn't occur when they took it for a test drive. They removed and
cleaned the HT leads and distributor cap but the problem has not gone away.