I know it's naughty, but I over invite people as I've I had this problem in the past. The 1st party we had for our dd we hired a hall and invite loads of people. Everyone said they were coming,but it ending up being family and a few friends.I wouldn't have hire the hall for a 9 people. Frustrating and the kids get so sad when their friends don't show up.
This year my daughter started reception class in Sept so I don't really know the parents, but I think I invited 12 people but I only expect half to turn up and that's what happened. 2 didn't even rsvp, so I was over my limit on kids, it was soft play and food,but the venue was cool about it. The venue held 25 kids, I invited 35 I know dangerous but I don't invite them all at once. First I invite all the people who will most likely turn up and get them to rsvp, and the ones who can't make it or don't reply I invite someone else in their place (With school I asked the teacher to put the invite in the child's book bag). The week of the party do a text around(reminder etc) to get a good head count.
Also try and attend all the other kids parties.
So this year I pulled off a good party, but no more parties until she's 12 or something.