I think you may interested in reading the following report....it documents how all 4 engines on a 146 rollbacked in flight and bacame a very expensive glider with passengers onboard.
"The investigation determined that during high altitude cruise, the aircraft entered an area of moist air significantly warmer than the surrounding air. This resulted in a need to select engine and airframe anti-ice which in turn placed high bleed air demand on the engines. Under these conditions the fuel control units were unable to schedule sufficient fuel to the engines, thereby causing them to lose power, a phenomenon known as ‘roll-back’."
Summary :
http://www.basi.gov.au/acci/jjp.htm Report :
http://www.basi.gov.au/pdf/vh-jjp.pdf