It is, yes. Needs some time to pass and for you to raise your (or is it the school's?) rep sufficiently.If a mother removes a girl from a school, is it possible to recruit the girl again in the same run?
Though you should be able to avoid losing girls by raising their int sufficiently (using home visits) combined with the right homework, not adding too many new girls at a time, assigning girls most in need of grades to the classroom, and/or making use of rule breaks to get the mother to forgive the warning.