Re: au pair agencies
Usually there's a period during which an agency will refund all or a part of a fee paid if a placed employee leaves of their own accord. From my experience, it's anywhere between 1 month and 1 year. It doesn't depend on the length of the particular engagement (I've only really seen terms where refunds are offered outside of a 3-month period from start date for placements for an indefinite period and for pretty senior positions in companies). I've seen different terms from lots of different agencies (employment agencies work similarly). The standard term in my experience is that there's a decreasing refund up to 3 months (e.g. 75% if employee leaves month 1, 50% if they leave month 2, 25% if they leave month 3).
If you had a contract with the agency, that will tell you what rights there are to a refund.
If you don't have a contract, then I'd say you are out of luck because it sounds like the parting of ways was more to do with circumstances happening between the two of you, rather than anything (such as lack of qualification or misrepresentation) to do with the agency.
I would think it very unusual for a placement fee to be refundable for the entire period of a fixed term placement (for a year, in your case). Fees are generally a finder's/placement fee as a %age of anticipated annual pay, or less if you are looking for a shorter period (as you are now). That fee is related to the placement only - it's not like a temp worker where the agency charges a %age of fees paid week-to-week. The placement fee is for the introduction only - after that, you're more or less on your own.