I had this with DS2 a few years ago. Not a deposit, but you HAD to give a month's notice, and if you didn't then you still had to pay for a month.
The Sole Trader shop I was employed in shut down. I got the sum total of 3 days notice. My wages stopped INSTANTLY. As did my WTC that covered the majority of the fees. (There's a run on now, there wasn't then).
I ended up owing the Nursery £2,000 for a service I hadn't used.
IMO, it should be pay by day. No sodding notice period or stuff like that. For NMW people like me, we just CAN'T cover childcare fees if our work stops or drops overnight.
Zero hours contracts are awful for this - I found I had to pay for the Nursery even when he wasn't there. How the hell am I meant to do that if I have no work that week, and therefore no wages?!
And THAT is why do many Lone Parents who would be working NMW jobs are on benefits. Because they can't take a zero hours contract because they still have to pay for Nursery or a Childminder when they AREN'T at work, and have NO INCOME. And they can't use a Nanny, because they aren't Ofsted registered, so they couldn't claim the help with costs from WTC that is essential if you are on NMW, and they often can't use an Au Pair because a) They have no spare room in their home, and b) If they had an Au Pair live in their home, they would breach the Tenancy Agreement if their home, and lose their home. (Subletting rules).