In the event production on the leasehold shall cease at any time or from time to time, after the expiration of the primary term of the lease, the lease shall nevertheless continue in full force and effect if the lessee shall, within 6 months after the cessation of production or within such longer period of time as the Secretary may authorize, commence and thereafter prosecute with reasonable diligence drilling, deepening, repairing, redrilling or other operations for the restoration of production of oil, gas, sulphur or other minerals from the leased lands.