I grew up playing by ear, and my Mom plays by ear, so I had been under the impression that because of my own upbringing, I would be more sympathetic to individuals who also only (want to) play by ear, as well. But, it's the opposite, in fact. I agree it is limiting if there is no ability to read or think through fingerings, but what it comes down to for me, I've realized, is that I simply have almost zero patience for individuals who say they play by ear but can't actually pick out a tune on their own. That is different.
Growing up, I heard the music and figured it out myself, and recently during a visit with my Mom, I could sing a tune once and she could figure it out almost instantly on her own on the piano. I also taught myself to read, completely on my own and had the desire to learn how.
I am not fundamentally opposed to people playing by ear, but I have a difficult time if they do not have pitch memory, note-grouping memory, and a basic understanding of how to find those on the piano - or at least zero real desire to cultivate these, which I actually believe are important to cultivate whether the individual reads music or not. If you absolutely need the students, keep her on and do whatever you possibly can, but if you can let her go, let her go.