The HSY teachers will be cycled through and replaced now and then, no matter what you do.
I really liked the Class 1 teacher, and turned off story progression so she wouldn't find a new job. Still, one day she'd been replaced. I went to the Households bin and deleted a bunch of randomized townies, including the new teacher, and the next day, my teacher was back. Once in a while, she gets replaced, and I do the same thing.
I was surprised to see the principal replaced, though! It doesn't seem to have anything to do with housing status.