The rule is that l’ (elision) takes precedence over au (contraction).* The second pair will combine first if possible, in which case the first pair will not.

Hence, what’s “hidden” by that apostrophe is not the a of la but the e of le !

The exact same goes for du vs. de l’. That is, de l’estomac, not du estomac.

However, it doesn’t affect aux and des since the elision is not available for les, so the contraction wins. So aux estomacs, des estomacs.

_{* That would be analyzing it in terms of rule order. Another analysis would be that the article and the noun are more tightly bound than the article and the preposition, i.e. they form a smaller unit.}

_{A third analysis would be to compare the outcomes at the word boundary: either two vowels /o ε/ (hiatus) or vowel-consonant-vowel /a lε/. LPH argues that French prefers the latter (consecutive vowels are the same thing addressed by liaison).}

The reason is that two consecutive phonétic vowels are rather very consistently avoided in French ; therefore, in the singular of nouns beginning with a vowel, instead of choosing the usual contraction, « au », the full form is chosen, in its elided form as the next sound is a vowel. In the plural the contracted form of « à les », which is « aux », as it ends with « x », is not a problem because then the liaison can be effected, and « aux » is pronounced /oz/.

• à l’estomac, à l’étang, à l’étayage, à l’été, à l’humeur, à l’exploit,…
• aux estomacs, aux étangs, aux étayages, aux étés, aux humeurs, aux exploits…