Laffin will be assuming the office of current GSG President Annie Rappeport.
Adam Rosenbaum wants to see more students voting in College Park elections.
The body's legislature for this session is also one of the most diverse in recent years.
The board felt it no longer had jurisdiction over the appeal due to the start of the 2020-2021 legislative session.
Several members of the body are pushing for an emergency meeting to override the veto.
The meeting lasted nine hours.
The appeal centered around social media posts the party and its supporters had made.
Voting closed Friday at 4 p.m.