Old Fiesta stalling after stopping

Hello.  I've an ancient 2003 Fiesta Zetec 1.4.  I've sort of grown attached to it, and want to keep it going for as long as possible.  It's been a good car, mostly runs well, and I want to look after it.  I can solve most problems, but something is wrong that is a bit of a puzzle.  Recently, it has started stalling when coming to a stop - sometimes it recovers, sometimes I have to restart.  I assumed it would be the PCV hose, but that turned out to be okay.  Next, I tried cleaning the throttle body, but that made no difference (and it was pretty clean anyway).  Today, I connected forscan to it to read the O2 sensor output voltage.  It seems within the normal range (<= 1V), but although the voltage can rise instantaneously, it takes about five seconds to come down again.  I don't know if I'm looking at a cause (faulty sensor), or a symptom of something else (e.g. clean, but still stiff throttle body).  Can anyone suggest anything?