Additional security deposit in the middle of lease term?

[Naga A.]

A tenant failed to pay a rent in Jan, and since then all our collection efforts were failed (he made all the executed, promises were broken and phone called were ignored etc.).  An eviction proceeding was initiated, and after we got a court judgment and just before kicking him out, the tenant all of sudden showed up at my management company's office and finally made all the payments owed to me.  

The problem is I do not trust this tenant any longer and anticipate that he will miss a payment soon and that we will have to do the eviction again.

My question is whether I as a landlord can ask for an additional security depost (about month rent?) to protect my interest from this tenant in the middle of term of lease because of recent eviction incidents.  The lease agreement is silent on whether I can do that.