Does a leasing agent have the right to hold my security deposit when they no longer hold the property?

The property manager "may" be able to hold your deposits. That answer is not addressed by statute, it is normally addressed by contract. Your lease may state what the property manager may or must do if the property manager stops managing the property during the term of the lease. Alternatively, the property management agreement (which is between the property manager and the owner; you are not legally entitled to a copy) may state what the property manager must do with your deposit. Having said that, send a letter to the property manager asking for return of your refundable deposits and see what kind of response you get. I know some property managers who send the refundable deposits back to the tenants even thought the property manager was contractually obligated to send it to the owner.