I would apologize for going back on your word and explain why. They need/deserve to have the chance to leave if they need too if they can't afford your new rate.

At the most, a child is with me a max of 4 years (unless they go on mat leave and stay/return) so I also tell parents the rate they sign on with is a fixed rate. If I need to increase (which I have), I increase it for new families coming in