How many times in one year can a renters rent be raised in the stata of n.m

It depends on the type of lease. If there is a written lease then the rent must remain the same and cannot be increased for the term of that lease (unless the written lease allows for increases). If there is no written lease then the tenant is a month-to-month tenant and the rent can be increased every 30 days as long as the landlord provides the tenant with at least 30 days advance written notice.