Lease agreements don’t generally terminate on the death of the landlord. The appointed executor of the estate of the deceased will take over the administration of the estate and transfer the residue of the estate, after paying out legatees, to the heirs. The rights and obligations in terms of the lease agreement will pass to the heirs, provided that the heir/legatee accepts the inheritance.
The terms of the lease agreement will be paramount in determining the grounds for termination of the lease. Should the agreement specifically provide that the lease terminates on the death of your father (the landlord) then this position will apply when the landlord dies. A tenant will however have to be allowed a reasonable period to vacate the premises.
Given that tenants could be affected by the death of your father, it may be prudent to approach your executor to review the lease agreements and determine the termination provisions thereof to avoid continuing uncertainty in this regard and ensure proper communication with your tenants on their continuing rental position.