You should argue that if your landlord no longer wished to accept late payments, she should have given you some advance notice. Obviously, relying on a judge to rule in your favor in an eviction case is often not the best choice. If you lose in court you may not have very long before you have to move, and you will have an eviction suit on your record. Even if you win in court the relationship with your landlord will be strained. Sometimes it is best to consider complying with the landlord's request to vacate especially if the landlord will allow you out of the remaining term of the lease, and will refund your deposit.
Landlords can also charge additional fees for each day the rent is late.
Generally, the total amount of late fees in any one month should not be more than half a month's rent. But again, a court could consider higher fees to be acceptable or lower fees to be unacceptable, there is no sure answer. A landlord sometimes deducts late fees from a tenant's rent and then claims the tenant is behind on rent again. Then the landlord charges late fees all over. There are no state laws that specifically address these activities.