I think some parents feel awkward coming into your home/daycare and therefore just say they love it and want to start to please the caregiver in person. Once they leave and reflect on their visit they may decide it isn't the best fit. At this point it would be polite to let the caregiver know (even just in an email) but that isn't always the case, some people prefer to just cut communication.
Don't chase people down. Let them know that you are willing to offer them a space and they have until XX date to sign a contract if they want it. Then leave it in their hands.
Do not look desperate for them to sign on and try not to make it seem like they are your only hope of filling the space.
I let all families know that I am interviewing others and will let them know if I feel they are a good fit after I have met all my families (whether there are more families or not). I never ask a family to commit while in my home. I do not ask them if they like my place etc. They HAVE to go home and think and reflect. The last thing you want is a family that isn't a good fit.