No person, firm or corporation shall appeal the same determination more than once in any twelve-month period. However, the Board of Appeals may, after a unanimous vote of all members present, rehear any order, determination or decision of the Board of Appeals. Such hearing is subject to the same notification provisions as an original hearing. Upon such rehearing, the Board may reverse, modify or annul its original decision upon a unanimous vote of all members then present, provided that the Board finds that the rights vested in persons acting in good faith in reliance upon the reheard order, decision or determination will not be prejudiced thereby.