Boeing have recently given some advice on this. There have been a number of unexplained flame outs over the years and the subsequent investigations could find no cause. It is now thought that it is due to ice crystals melting on contact with engine parts and cooling them to the extent that the water re-freezes on parts of the engine that the anti-ice can do nothing about. It was recognised several years ago that this could be severe enough to cause flame out in smaller engines but it is now thought that it can affect big engines the same way. Of course the ice melts again at lower altitude so is not apparent later. Turning the anti ice on has beneficial effects even if it does not stop the ice forming. The increased bleed air makes the engine more stable and as mentioned above turns on the ignition in a lot of models.
One of the danger signs is seeing moisture on the windshield even at temps below -40. This is not super cooled water but the very fine ice crystals melting on high speed contact with the heated glass.
Boeing now also recommend that in conditions such as these you put the wing anti-ice on as well, but only below 22,000ft in the descent. This again is to increase the bleed air take off. They don't recomment the use of wing anti-ice (unless for its proper pupose) any higher because there may not be enough bleed air available for other systems that need it.
The other obvious advice is to avoid areas where this may be a problem (ie as stated above, near convective cloud at high levels) or if already in them get out sharpish.
TC