I think kids can be cliquey and there are a variety of reasons she could be being left out.

My first thought is this school based? Are there after school hobby groups she can join (away from the school)? This could introduce her to a whole different dynamic of kids who may not be as cliquey. Our son joined the Scouts and it was great for him, he became more confident and met a wider bunch of people.

I think much as it is breaking your heart it will be really important to keep positive for her - every day being a new day and not to be disheartened. Keep on encouraging her and keep up inviting children she likes over (one to one), it's important to remember this is a phase and she will come through it.