I admit to reading only 66% of this thread so perhaps I might have missed something. Apologies if this is the case.
It is well known that the CFM56 fan is neither capable nor certified to tolerate bird strikes of a size such as occured in the case of US Airways Flight 1549. A little research reveals that earlier CFM56 fan sets suffered from resonance and high-cycle fatigue. And in addition, rain/hail ingestion has also given rise to several incidents with this engine.
Perhaps what is generally less well known is that CFM56 fan blades have been observed to suffer significant damage in the event of ice accretion. When this occurs, high levels of N1 engine tracked order vibration are likely to be observed, along with audible changes in engine 'tone'. The consequences of prolonged engine operation in this condition merit little discussion.
The following report therefore, although not conclusive, contains some degree of credibility:
AirAsia Flight 8501 Crash Possibly Caused by Icing, Indonesian Report Says - WSJ
Are A320 and B737 pilots routinely trained in ice shedding manouvres, and what is the policy for avoidance of potential ice accretion?
By way of explanation, my personal backgound is in aircraft and engine prognostic health monitoring, including engine bird strike detection and fan blade damage detection.