To get around this I created a one page form that has parents name, address, phone on, anticipated days and hours and starting date for care and that page must accompany the deposit. The contract itself and the actual information forms can be done closer to the start date but the page and money confirms space. Paying the deposit is equivalent to confirming the space and therefore I would think they would be bound by the contract and that legally they have up to the starting date to have a signed copy of contract on file but they paid the deposit as per the contract meaning they understood the terms they were paying under.
If she had said in January that they were no longer interested that is one thing but to wait this long is not fair to you and no they do not get their deposit back.
I have done a couple interviews for september already and the people that came seemed paranoid to secure a space and I made it very clear to them that paying the deposit is final and that once paid it is not returned even if they come back next week months before the start date. The deposit is not something you pay to "hold" a spot while you keep looking just to make sure you have one. That once paid I stop interviewing and the money paid compensates for having to start over again. Needless to say they didn't pay.