A333 : by Tony Garland 
I can't give you a “biblical explanation” as to why the verse is included in some translations and not others (since the bible itself doesn't give us information about the various Greek manuscript families). But, what you are seeing is difference in opinion by the translation committees for the different translations as to which manuscripts (or manuscript families) they view as more reliable (closer to the original Greek autograph).
Many modern English translations give the largest weight to a couple of early manuscripts (א and Β). They take the approach that oldest must be nearest to the original and therefore the most reliable. The oldest manuscripts do not include Matthew 17:21 (and omit “fasting” in the parallel verse at Mark 9:29). So English translations based on the oldest Greek manuscripts follow suite. An exception would be the NASB and HCSB (now CSB) which include the verse, but place it in brackets: indicating they prefer the older manuscripts, but also deem the variant to be important enough not to relegate it to a footnote.
Other translations, such as the KJV and NKJV, have a different philosophy regarding manuscripts. They do not assume that the oldest manuscript is necessarily more reliable and follow the "majority text" (MT) manuscript family—which includes Matthew 17:21 and mentions prayer and fasting in Mark 9:29. This philosophy of translation, in simplified form, sees the majority of manuscripts as a better witness to the original autographs than the oldest.
I discuss the topic of manuscripts in greater depth in one of my previous Q/A answers: Q327 - The Identity of the New Testament Texta.
Hope that helps! - Tony
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