Upon motion initiated by any member and adopted by not less than a majority of all the members of the Board of Appeals, the Board of Appeals shall review, at a rehearing held upon notice given as upon an original hearing, any order, requirement, decision, interpretation or determination of the Board of Appeals. Upon such rehearing, the Board of Appeals, upon the vote of not less than a majority of all of the members of the Board of Appeals, may reverse, modify or annul its original order, requirement, decision, interpretation or determination, as long as it does not appear that the rights vested prior to such action in persons acting in good faith and reliance upon the original order, requirement, decision, interpretation or determination will not be prejudiced.