"Each other" is like that for me, and according to search results, a lot of other people. I pronounce it ee-chother.

"Eachother" feels as natural as "somebody", "nobody", "anybody" to me

Because of the vowel following consonants, my mind splits that word into these syllables: Ea-cho-ther, so not as natural as those other words. Then again, it's English, the only rule is there's no rules.