Why is the "r" doubled in "arrhythmia" relative to "rhythmia"?
I'm guessing it's because English resists hyphenation of prefixes and suffixes ("a-rhythmia"), while direct prefixation by "a" would imply the wrong pronunciation: "arhythmia" looks like it should be pronounced "ah-rhythmia". However, "arrhythmia" also looks like it should be pronounced "ah-rhythmia", so that doesn't explain things...
I can't think of other cases that double the initial consonant when preceded with "a": the antonym of "tonia" is not "attonia" but "atonia", for example. The antonym of "regular" is "irregular", but the prefix is, I think, considered to be "ir", not "i". Maybe that simply means that the antonym prefix of "arrhythmia" is "ar", not "a", even though the word is pronounced "'A'-rhythmia", not "arr-rhythmia"?