Like most "what happened to fairies" generalizations, there isn't a one size fits all answer, because "fairy" is a term that applies to a whole bunch of different mythical creatures from different cultures with different histories. The process of lumping all these creatures together into one mythos for use in fantasy stories and role playing games is a later development.
Some cultures already had a tendency to present certain supernatural creatures as diminutive, such as Cornish pixies or Germanic trolls, though even here, diminutive stature wasn't always a feature of these creatures. Sometimes they were depicted as normal human height.
Others depicted fairy-like creatures as being capable of growing and shrinking at will, and so individual stories might have tiny fairies, but that wasn't some fundamental feature of them. To make matters more complicated, some cultures used terms like "wee folk" to describe fairies, despite not tending to depict them as diminutive initially, as a sort of polite descriptor to describe spirits diminutive in power compared to the divine after they began to be syncretized into Christianity.
Within some of these places, more recent local folklore even tries to explain the "shrinking" of the wee folk as a consequence of the old gods becoming small after they stopped being worshipped. While this is not literally true in the way some of the folk sayings suggest, there may be a process by which some fairies in narrative gradually diminished in both power and physical stature over time following the advent of Christianity. There is an interesting theory out there that the leprechaun is a diminutive version of the deity Lugh that shrunk and changed over time following the conversion of Ireland.
As fairies became the purview of Victorian children's authors, their diminutive stature became standardized. This may be part of the process of making these creatures that could be genuinely dangerous in their original depictions more "kid friendly", or as a way of explaining why you don't see fairies running around, or both, or neither, but during this time you start to see standard images of fairies, recognizable to modern eyes, showing up.
So it's kind of both. There are depictions of diminutive fairies in early folklore, and the tendency to represent fairies as diminutive increased and spread over time, but the idea that this applies to all fairies all of the time didn't develop until much later.