Do long vowels ever get reduced to schwa?

I was taught that any vowel can get reduced to schwa if it is unstressed, but I can't find any examples of a long vowel getting reduced to schwa. Is it only short vowels that can become schwa?

The term "long vowel" doesn't refer very clearly to a particular set of vowels in English. However, whatever is meant by it, I'm fairly sure that it is true that long vowels can get reduced to schwa in fully unstressed syllables.

Not all unstressed syllables permit vowel reduction

First, I'd like to make a few clarifications about the statement "any vowel can get reduced to schwa if it is unstressed". This is definitely false if it means "any vowel can get reduced to schwa in any unstressed syllable": only some kinds of unstressed syllables are subject to vowel reduction. Word-final vowels in unstressed syllables are often not subject to vowel reduction, except for in non-standard varieties (or perhaps in "fast speech" of standard varieties where other kinds of reductions that are not typically noted can occur). For example, as a rule, the word-final unstressed vowel in words like shallow, hero, grotto cannot be reduced to schwa in a standard English accent.

Some varieties of English also have a tendency to reduce front vowels to /ɪ/ instead of reducing them to schwa. For example, in some accents the unstressed and reduced first syllable of the word evolve is pronounced as /ɪ/ rather than as /ə/.

In the contexts where reduction is possible, it is often optional.

Examples of "long" vowels that may be reduced to schwa: /(j)uː/, /oʊ/, /ɔː/, /ɜː/

One vowel that is conventionally thought of as "long" is the "long u" vowel, which in stressed syllables can be transcribed /uː/ (or with an onglide included, /juː/) with the length marker ː. In unstressed non-final syllables, /(j)uː/ can be reduced to either /(j)ʊ/ or /(j)ə/. Some example words where this optional reduction can occur (the frequency and degree of reduction varies between speakers): accusation, permutation, reputation, immunize.

The vowel found in words like goat is classified as a "long vowel" according to the traditional English definition: it is often called the "long o" sound. It tends to be transcribed as a diphthong /əʊ/ (British English) or /oʊ/ (American English), although for American English, the single-letter transcription /o/ is sometimes used. This vowel may be reduced to schwa in word-internal unstressed syllables, as in the word int[ə]nation.

Words spelled with or followed by a consonant are also typically classified as containing vowels that are long when stressed: e.g. north and force (some accents use different vowels in these words, but in the most well-known accents they have the same vowel, which can be transcribed as /ɔː/ for British English or /ɔːr/ for American English). This vowel can be shortened in an unstressed syllable: for example, information can have schwa in the second syllable (in American English, the following /r/ would phonetically color the schwa or turn it into a syllabic r sound), in contrast to the unreduced vowel found in the stressed syllable of the verb inform.

Likewise, the vowel represented by er, ur, or ir followed by a consonant is typically classified as long in British English when it occurs in a stressed syllable: bird, burn, term can be transcribed as /bɜːd/, /bɜːn/, /tɜːm/ (or /bəːd/, /bəːn/, /təːm/). But in an unstressed syllable, this may be reduced to a short schwa, as in preservation (OED transcription "/ˌprɛzəˈveɪʃn/") in contrast to the verb "preserve" which is transcribed in British English with a long vowel (OED "/prᵻˈzəːv/).

Diverge

Pronunciation: /dəˈvərdʒ/, /daɪˈvərdʒ/.

You won't find vowels in stressed syllables reduced to schwas, but there are lots of English words with long vowels in unstressed syllables.