DAve TS, it is because the ash will accumulate on every thing and at the same time be very abrasive (think of sand blasting and you will get the idea).
The ash will accumulate in the flame cans (where the flame is held) inside the engines and eventually turn from ash into glass and stick to everything inside the engine.
Thus starving the flame cans of air and extinguishing the engines.
Once the flame goes out the glass will cool solidifying even more but becoming brittle as well.
If the pilot is lucky they may be able to shed the glass and restart the engines.
This is what (I believe) happened back in 1982 near Indonesia.
If I am wrong then please correct me.