Unless there are significant and material changes, parents are unable to have a second appeal within the same academic year for a place in the school. The relevant admission authority might have a policy not to consider repeat applications without a change in circumstances. If so, this must be published in the admission arrangements.
If there have been material or significant changes in your circumstances then the law expects the full appeal procedure to be adhered to (see School Admission Appeals for Primary schools).
The admissions authority is able to decide whether your fresh appeal should be before the same or a different panel.