They need daycare now for their child...they chose you. It may have only been until a space in a center is open but that is what it is. It does suck, but you currently have a client.

I think it is unprofessional to terminate them merely because they will eventually switch to a center. And, I do believe that in time word of mouth and reputation will come back to bite you for doing that.

There are never any guarantees as to how long a child will stay with us. The best you can do if you do not want families that only want short term care is to screen them out to the best of your abilities. Ask direct and indirect questions to attempt to figure out their long term plans. Keeping in mind that those plans will change in many ways (new job, move etc).