Does being passed over this year increase my chances of acceptance the next year?

Not necessarily, although it will be borne in mind. The applicant pool will change each year, and we want a good mix of dancers each time. If we are overwhelmed with applications, some dancers who have attended many or all Fried-For-Alls or Lenox Assemblies may be asked to take a year off, in order to give others the chance to attend this weekend.