The shortest length of time I had a child in care was ONE HOUR! The mom had been bringing the baby for short periods for over a month and everything seemed fine - baby was only 5 months but that was normal back then.

Well we got to the actual start date when mom had to go to work. She dropped baby off fine but instead of going home for a bit or shopping or any of the things she had done the past month she sobbed all the way to work - went straight to the manager's office and said she just couldn't do it and quit. She then sobbed all the way home and came to get the baby. Manager tried to give her another chance but she just couldn't do it. She ended up staying home with the baby an spent most of her time trying to be as frugal as possible to help make ends meet.

My guess is this could also be what you are dealing with in that when it came time to actually start the mom has changed her mind. The other thing that could have happened is that family members stepped in at the last minute such as grandma and offered to care for the child and now the family doesn't know what to tell you or what their obligations are. They won't be thinking of notice required since they didnt' even start care. The deposit is non-refundable so that is yours to keep and I would just move on. If you can find someone I wouldn't be giving them a second chance.