One of the requirements for remaining in the Honors Program is that students must maintain a 3.5 GPA. If a student in the Honors Program has their overall GPA drop below 3.5 for one semester, they will be put on probation. If their overall GPA remains below 3.5 for a second semester, they will typically be dismissed from the Honors Program.
It is possible to appeal your dismissal from the Honors Program. Appealing your dismissal basically involves sending the Honors Program Directors an email detailing: (1) why you want to stay in the Honors Program, (2) how you plan to raise your GPA, (3) how you plan to complete the requirements for the Honors Program, and (4) what benefits you believe you’ll receive by remaining in the Honors Program. Once the directors have that information, they will evaluate it and make a decision.