The Texas Apartment Association offers some information on late payments of rent.
The landlord has the option to follow legal means for eviction for nonpayment of rent or late payment of rent if not paid on or before the due date. Though it may be difficult for the landlord to evict a tenant for paying rent on the second day of the month, the best policy for a tenant is to be in the habit of paying rent by the date due.
If the rent is going to be late, the tenant should contact the landlord and attempt to reach an agreement with the landlord to get the rent current. It is best for the tenant to get a clear agreement in writing that the landlord will accept the late rent on a certain date and, in exchange, will allow the tenant to continue under the original lease agreement. This is a protection for the tenant because if rent is paid late and accepted, the landlord can still proceed with the eviction process for breach of lease due to late payment of rent. There is no requirement that a landlord give a tenant a grace period to pay delinquent rent.
If the landlord accepts late rent before giving the tenant written notice to vacate for failing to pay rent on time, the landlord gives up the right to evict for late payment of rent.
The landlord may be prevented from evicting a tenant if a pattern is established of accepting late payments from the tenant. The tenant’s proof would be the dated rent receipts. For the landlord to require the tenant to begin paying on the due date, the landlord should clearly inform the tenant that the landlord will not accept future late payments. Thereafter, if rent is paid late, the landlord could follow the eviction process for breach of lease due to late payment of rent. The exception to this would be if there is a “no waiver” clause in the lease agreement which would explain that the landlord can accept rent after due date. But in accepting it, the landlord would not waive his right to evict for breach of lease for late payment of rent even though the tenant may have had a pattern of paying late rent.