It is true that this happened to BA
on 24 Jun 1982. The 747-236B G-BDXH flew through the plume of a volcano eruption.
It takes quite a bit of ash and smoke to actually shut down the engines, so this plane was at once supremely unlucky, and then supremely lucky to recover. The plane was a glider from FL370 down to FL130 and still only got 3 engines to stay lit.
This also happened to a KLM 744 on 1989.
See here for more info: http://aviation-safety.net/events/WXA.shtml
This is in no way frequent, but I guess there is some theoretical potential wherever there are active volcanoes.
"There are no stupid questions, but there are a lot of inquisitive idiots." - John Ringo