One well-known example is the changes to vowel harmony in Korean, from the Middle Korean period (13th-15th centuries) to the modern day.
In Late Middle Korean, the yang/bright vowels were ㅏ /a/, ㆍ /ʌ/ and ㅗ /o/, while the yin/dark vowels were ㅓ /ə/, ㅜ /u/, and ㅡ /ɨ/. The vowel ㅣ /i/ was neutral. There is some debate on the precise realisations of these vowels, but the vowel harmony itself is consistent.
There have been many vowel shifts that have happened to [Seoul] Korean since then, with ㅓ /ə/ moving towards /ɔ/, ㅗ /o/ becoming closer to /u/, and ㅜ /u/ fronting to /ʉ/, not to mention what's happened with compound vowels. But overall, these changes did not hugely affect the pattern of vowel harmony in verb conjugations or in word derivations. Indeed, Modern Standard Korean retains vowel harmony in certain verb forms, even though the 21st centuy sound of ㅓ may be very different to what it was in the 16th century (and potentially closer to what the 15th century yang vowel ㆍ used to be).
However, the complete loss of the vowel arae a ㆍ /ʌ/ as well as the increased use of non-harmonising loanwords (mainly from Late Middle Chinese) dramatically eroded productive vowel harmony. This is especially relevant in nominal morphonology, where ㆍ was used in the yang forms of many particles.