Sappho wrote in the Aeolian dialect of Greek, which fell out of favor in Greek academic curriculums in favor of Attic and Homeric Greek by late antiquity. By Roman times, one had to have an esoteric knowledge of Greek in order to understand her, much the way an average English reader would be challenged today by Middle English. Let Dartmouth classicist Margaret Williamson (in The Classical Tradition, Grafton, Most & Settis, 2010) explain:

Like most other early lyric, her texts did not survive in a direct manuscript tradition, probably because of factors such as the perceived obscurity of her dialect rather than, as some sources claim, because of censorship by Christian emperors. The latest surviving copies, on parchment [as opposed to papyrus fragments], date to the 6th and 7th centuries CE; for most of the early modern period her poetry was known only through quotations in other authors, first collected under her name by Henri Etienne in 1560.

There is no reliable evidence that enough of her works survived to be burned in 1703 by the Catholic Church. In fact, the Greek father of the church Gregory of Nazianzen (d. 390) seems to know and quote her approvingly.