The root aer- used to be pronounced with a hiatus, but this seems to have become mostly archaic. Peter Shor mentioned this in some comments with a link to the Webster's 1892 International Dictionary, which shows the pronunciation of aërial as /eɪˈi.ri.əl/.
I don't know for sure why the pronunciation changed to have /ɛər/. Here's some speculation. It looks like in most words, the "a" was stressed and the "e" was unstressed: for example, the pronunciation for aëroplane is given as /ˈeɪ.ər.oʊ.pleɪn/~/ˈeɪ.ər.ə.pleɪn/. It's fairly easy for /eɪ.ər/ and /ɛər/ to interchange. We see this sort of variation in the words prayer and mayor, for example (although this is not quite the same situation; in these words the monosyllabic pronunciations are actually quite old and may be partly based on sound changes that occurred in French). If we look at other vowels, we can find similar examples of coalescence that definitely occurred in English, such as the pronunciation of drawer as /drɔːr/ and the pronunciation of theory as /ˈθɪəri/.
This type of "smoothing" change wouldn't normally affect a word like aërial where aër- was pronounced as /eɪˈi.r/ rather than as /ˈeɪ.ər/. The /eɪˈir/ pronunciation seems to have been replaced by analogy with words like aeroplane (where smoothed /ˈeɪ.ər/ was reinterpreted as a single syllable /ɛər/). It seems likely the pronunciation of the related noun air as /ɛər/ also influenced this development.
If we look at entries for aerial in modern online dictionaries, we can see the pronunciation /eɪˈi.ri.əl/ is not quite dead: it's still listed by the American Heritage Dictionary, Merriam-Webster's Online Dictionary, and Dictionary.com (which is based on the Random House Dictionary). But it's clearly not the main pronunciation: all of these dictionaries list /ˈɛər.i.əl/ as the first pronunciation for the adjective and the only pronunciation for the noun, and in many other dictionaries this is the only pronunciation listed for both parts of speech.
Another word spelled with "ae" that "should" have hiatus, but that has developed an alternative pronunciation is aeneous, from Latin aēneus/ahēneus. The Oxford English dictionary indicates that it may be pronounced with hiatus between the a and e, in accordance with the etymology (UK /eɪˈiːnɪəs/, US /eɪˈiniəs/) or it may be pronounced as if the ae came from a Latin diphthong (UK /ˈiːnɪəs/, US /ˈiniəs/). Merriam-Webster and the American Heritage Dictionary only mention the pronunciation with hiatus, and Collins only mentions the spelling pronunciation with ae = /iː/.