With the 'reference' are you meaning asking a current/past client to give YOU a reference for advertizing purposes or you asking if it is a good idea to ask the prospective CLIENT to provide contact info of the previous or past providers as part of your interviewing process?

I answered initially based on the former cause that was the way I read the post ~ it sounded like you have a perspective client whose child has been in daycare and you were wanting to know the 'background' on why they are leaving before committing to accept the child.

If you are meaning asking for people to give YOU reference on your business and program ~ than yes that is a good idea too I regularly ask my clients to do this for me typically as they are 'leaving' with the written references so that I can keep my references up to date as well as asking them to be my 'phone' ones anytime I am in the process of filling a space.