I don't mean this to sound harsh but in a way, yes they have been telling you when they will pay you and because it's been accepted they think it's okay and have continued to do so.

In my contract and on my payment schedule that every parent gets, it is clearly stated that if payment is late, they will have to find alternate care. I do not provide unpaid care so their bill has to be paid or else their child is not allowed here.

I have never had to let a family go either but if I do, yes I would be honest and tell them why.