Why does the NRSV-CE omit mentioning prayer and fasting in Matthew 17? The NRSV-CE omits mentioning prayer and fasting, explaining in footnote (g):


  Matthew 17:20 Other ancient authorities add verse 21, But this kind does not come out except by prayer and fasting


Rheims translation of Mt. 17:20, based on Jerome's Latin Vulgate, says:


  But this kind is not cast out but by prayer and fasting.Hoc autem genus non ejicitur nisi per orationem et jejunium.


Why does the NRSV-CE omit mentioning prayer and fasting in Matthew 17?
By "Other ancient authorities add verse 21, But this kind does not come out except by prayer and fasting" they mean that not all sources contain verse 21, and they come to the conclusion that it is a later addition and not originally there. So the translators omit the verse to be closer to the original text (which is unknown). It reflects a decision what sources the translators deemed more authoritative than others. Maybe because they are older, or there are more sources which confirm this reading.

I can't say anything about how justified this is in this particular case, but this is what should be understood from the footnote.