If the door does not work because it is old, and suffers from ordinary wear, the landlord mut fix it. If the door has been damages since you moved in, you are required to fix it. If the landlord refuses to honor the repair obligation, you should write to the landlord explaining that if the door is not repaired shortly (provide a date; 5-10 days is reasonable), then you will retain a repairman and deduct the repair costs from next month's rent. Be sure to include a copy of the receipt with your rent payment
See the information at the following link.
Repair and deduct at your own risk. Remember, your LL holds your deposit. It seems the wiser course may be to tough it out for the balance of your 60 day tenancy.