I'm going to ask @PanelChair @admission and @prh47bridge to take a look at this thread, @Misschiff, as you've posted in an unusual part of MN for admission queries.
If I understand correctly, when you first applied, you were told that the school had a space, but they had too many children with SEN already, so it wouldn't be fair on the other children or the teacher to take your child because of her additional needs?
They are allowed to refuse admission if they consider that admitting your DD would be an inefficient use of resources or would prejudice the efficient education of other pupils. However, if you are appealing, you need to show that admitting your DD would 'not' prejudice the efficient education of other pupils.
The fact that they already have pupils with SEN will be a factor, but that is countered by the fact that they should have provision for those pupils. The fact that your DD only has 1 or 2 seizures a month is a factor in her favour, but one area that you need to consider is what level of additional care and supervision her plan says she needs, and the burden that would put on the class, including the infrastructure.
Some classrooms are quite cramped. 30 children, 5 with SEN, with 5 1:1 supports, for example, would take a room holding 32 people up to 37 people. That's an extra 5 chairs, etc.
You say it's gone to appeal with the church and been rejected. Did you have a hearing? Did you get a bundle of papers with the Admission Authority's written argument, PAN, Class arrangements, Capacity diagrams, etc.? Did you have the opportunity to state your case, to question the Authority's representative, etc?