I would have this discussion early-ish (6 or 7 months) if you're SURE you want to rematch. I usually start hunting for my replacement au pair around month 8, so at some point I need to know.
I think the key is to frame the request very very gently. Some girls, even if they love your family -- only plan on a year, and they will want to go home. If that is their feeling it is BETTER FOR BOTH OF YOU THAT THEY GO! Pressuring a girl to stay even a little can lead to real difficulties.
We had a lovely au pair one year who really loved our family, but felt torn about staying or going. She had a serious boyfriend who had waited for her at home for a year, and she finally said "he has waited long enough." I emphasized to her several times, that while we loved her, and would love to have her stay -- that we were so thrilled that she had given us a year of her life, and that if she felt it was time to go home, then we would support her. And we tried really hard to make sure we didn't "guilt her" at all, because she was already tearing herself up over it.
So -- my advice. talk early, but approach gently. Make it clear to your au pair that the reason you want them to stay, is because you love them so much... but also, because you love them so much, you will understand if it is time to go home.