Why does the pronunciation of the word "wife" [waif] change in the word "midwifery" [ˈmɪdˌwɪfərɪ]?

Alexander Ellis^† claims that the modern pronunciation [midwaif] is “orthographical”:

 -wife, midwife housewife goodwife. Here orthographical readers say (mi⋅dwə′if ʜəu⋅swə′if gu:d wə′if). But (mi⋅dif) is more common, and no actor would speak otherwise in describing Queen Mab, RJ 1, 4, 23 (717,54). The thread-and-needle-case is always called a (ʜəz⋅if), and the word (ʜə⋅zi), now spelled hussy, shews the old disuse of (w), and similarly (gu⋅di), now written goody. (1165) —On Early English Pronunciation, Pt IV (1874), 1165

Though the pronuncitation ['mɪdɪf] (in modern notation) is ignored by most old dictionaries, it is acknowledged here and there. Routledge's Pronouncing Dictionary of the English Language, 1867, gives two pronunciations, “mid′wif, or mid′wīf ”, and Walker, Critical Pronouncing Dictionary, 1791, gives

MIDWIFERY, mid’-wif-re, s 144 … Though the i is long in Midwife, it is always ſhort in its derivative Midwifery, and the compound Manmidwife.

And “144” refers to this note:

 144. Thoſe ending in ife, have the i long, except houſewife, pronounced huzzif, according to the general rule, notwithſtanding the i in wife is always long. Midwife is ſometimes ſhortened in the ſame manner by the vulgar. (42)

OED 1 (1906) says “the colloquial pronunciation (mi⋅dif) is now seldom heard.”

It appears that at least by Modern English the secondary stress on the second syllable of midwife had been reduced in non-educated speech to non-stress. This may have been the case even earlier, since Middle English spellings indicate that a variant was then current with the same connective vowel between the first and last syllables which gave rise to the /ɪf/ pronunciation in housewife and goodwife. Alternately, the reduction may have come about by analogy with housewife and goodwife.

“Polite” usage eventually succeeded in stamping out the “vulgar” pronunciation of midwife; but it may be suspected that ['mɪdɪfrɪ] was acceptable under the principle of trisyllabic laxing.

^† Prototype of Shaw's Henry Higgins and inventor of the IPA characters ʃ and ʒ (along with several other notations which have not survived)

Currently, both pronunciations are correct. Native speakers of English determine meaning and pronunciation. This descriptive approach irritates prescriptive linguists, but it usually prevails.

The stress and reduction depends on the length of the word as well as common practice. Compare photograph with photography.