I worked at 3 centers. One just for a day (it was a DANGEROUS place!), the other for a week (it was too chaotic for me) and the other for almost a year. The one I was at for about at year, I was a floater and worked in every room ages 6 weeks - school-agers, filled in as an aide or teacher in every room, the office, the kitchen, and helped with custodial work.
What they did there with the children who were a bit much to handle, was to send to the office when their teacher in their regular room had enough of the child. After being in the office for a while, they'd try to send the child back to his/her regular room. If that teacher still didn't want him/her back, they'd just flop the child from room to room as he/she drove each teacher too nuts and she kicked him/her out. But, at the end of the day, the child would ALWAYS be in his/her correct room and the teacher would tell his/her mother what a GREAT day he/she had.
They kept the children no matter what just to keep the money coming in!
That same center, however, had about 1/3 of it's clients in at least a month's arrears (behind in at least a month's worth of payments!) and they just let them keep coming and racking up back payments. I guess eventually, the parents would catch their payments up.