Old English missan "fail to hit, miss (a mark); fail in what was aimed at; escape (someone's notice)," influenced by Old Norse missa "to miss, to lack;" both from Proto-Germanic *missjan "to go wrong" (source also of Old Frisian missa, Middle Dutch, Dutch missen, German missen "to miss, fail"), from *missa- "in a changed manner," hence "abnormally, wrongly," from PIE root *mei- (1) "to change, go, move." Related: Missed; missing.
Meaning "to fail to get what one wanted" is from mid-13c. Sense of "to escape, avoid" is from 1520s; that of "to perceive with regret the absence or loss of (something or someone)" is from late 15c. Sense of "to not be on time for" is from 1823; to miss the boat in the figurative sense of "be too late for" is from 1929, originally nautical slang. To miss out (on) "fail to get" is from 1929.