Be sure to document the problem by taking pictures of the roaches in your unit. You should also make your requests for pest treatment in writing to management. You should also take photos to establish that you are keeping the unit clean and free of crumbs, empty beverage cans and bottles, boxes, etc., all of which may attract and contribute to a pest problem.
I will say that a judge will probably view the fact that management has sent an exterminator following each of your complaints as a positive for management. That said, you should not be expected to live with roaches for the balance of your lease, and if the problem continues, you should create an escrow account and notify the landlord that you will be depositing rent in escrow until the roach problem is satisfactorily resolved.Ask a similar question