I used to work in sales... we would follow up with potential leads 5 or more times, before writing them off as being a non-starter.
Follow ups I feel are important in many business sectors, including childcare. When you get an enquiry, obtain as much info for followup purposes as possible: Full Name, Phone Number, E-mail Address, Home Address - as well as all the usual childcare related questions such as ages of children, nursery/pre-school/school info, days/hours etc.
By arranging a visit, they have shown interest. Since visiting you, their circumstances may have changed, or they may not have liked you, or they may have just forgotten about it (especially if proposed start date was some time off).
Follow-up in whatever way you feel most comfortable. Personally, I follow up via e-mail (as I dislike the phone). Calling would probably get better results, but at least by following up via e-mail, I can try to establish communication.
Perhaps send a Thank You note... nothing long. Just a quick note saying something like:
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Thank you for visiting me on xxxx. It was great to meet NAMEOFCHILD/CHILDREN and yourself.
I would be delighted to care for NAMEOFCHILD/CHILDREN and can offer you x hours per week, starting from DATE.
Please contact me so that we can finalise arrangements, or discuss your requirements for childcare further.
If you are no longer looking for a childminder, please drop me a quick note, or give me a call.
Thank you again for visiting me and I look forward to meeting you again soon.
YOURNAME
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Hope that's of help.