Is it permissible to renew the lease agreement while retaining the previous security deposit, or must the previous security deposit be considered as rent for the next two months, and then a new security deposit be paid; in accordance with the Hadith: "No two sales should be combined in one transaction"?

There is no objection to writing a new contract while retaining the previous security deposit. This does not fall under the prohibition of "two sales in one sale," which has been interpreted as selling for two prices without specifying one at the time of parting, or making one sale contingent upon another.