Does not screening for critics happen often?
Of course, many films do that. Even in the related editorial.rottentomatoes.com discussion about Æon Flux, they listed a few films which were not screened For Critics:
- In the Mix (2005)
- The Fog (2005)
- Cry_Wolf (2005)
- King’s Ransom (2005)
- Cursed (2005)
And they got bad reviews from critics after release. But not all films not screened for critics are received badly. There are some exceptions like Psycho (1960), where the director wanted to avoid pre critic screening to maintain the suspense and it got mixed to positive critics response.
Why was Æon Flux not screened for critics?
I can find no official statement about it from the officials but Wikipedia listed two popular reasons for not screening for critics:
Critic (or "press") screenings are held for national and major market critics well in advance of print and television production-cycle deadlines and are usually by invitation only. This step may be omitted if a studio anticipates negative critical reviews, or if a film is still being edited until immediately before release.