Except for words imported from non-Latin/Germanic languages, words with ortography matching the following regular expression will have the matching part realized as /er/:  `*a[ei]r[iey]*` provided that the matching syllable has the word-stress.

In the "Shorter Oxford English Dictionary" the expression matches over 450 headwords with only a couple exceptions, like "Bohairic" (via Arabian), "dairi" (via Japanese), "etaerio" (From Greek via French; exception to the non-Latin precondition).  In the cases that I investigated Merriam-Webster's Collegiate was also providing the phoneme /e/ for the syllable that includes the letter "a".

It appears that if the consonant was not "r" then the realization would be most often /ei/ (as in "tale", "calix", "agave", "baby","navy", "zamia") but the "r" reduces that to the less heavy /e/.  The rise is likely related to the stressed syllable being open.

There exist other examples, with all requiring that the 'a' be in a stressed syllable but there appear to be more exceptions than matches in the cases that I investigated ("scarus", "marum", "larum", "garum",  --> /e/ but most other matches are a false positive).

This observation mostly matches the first comment of Janus Bahs Jacquet but strengthens the conditions for the raise to happen.  Will be glad to revise if someone is able to provide a condition that provides a higher accuracy.