Any special exceptions, variances or appeals authorized or granted by the City Council either under the provisions for this Ordinance or under the authority granted to the City 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 City Council, unless said City Council in its minutes shall at the same time, grant a longer period, or such extended period as the City Council may specifically grant, then the special exception, variance or favorable appeal shall be deemed waived and all rights thereunder terminated. Such terminating and waiver shall be without prejudice to a subsequent appeal to said City Council in accordance with the rules and regulations herein contained.