Any special exception, variance or appeal authorized or granted by the Council either under the provisions of this Ordinance or under the authority granted to the Council under the statutes of the State of Texas shall authorize the issuance of a building permit, or a certificate of occupancy, as the case may be, for a period of ninety (90) days from the date of the favorable action on the part of the Council, unless said Council in its minutes shall, at the same time, grant a longer period. If the building permit and/or certificate of occupancy shall not have been issued within said ninety (90) day period, or such extended period as the Council may specifically grant, then the special exception, variance or favorable appeal shall be deemed waived and all rights thereunder terminated. Such termination and waiver shall be without prejudice to a subsequent appeal to Council in accordance with the rules and regulations herein contained.