Tax exempt rules will vary by state or local jurisdiction.
In Texas, the regulation is:
Permanent Residents
(30-Day Rule)
Guests who occupy a hotel room for 30 or more consecutive days are considered permanent residents and are exempt from hotel tax. There can be no interruption of payment during that period.
Colorado
If a company rents a room for 30 consecutive days, but four different people from that company stay in the room, each at different times within the 30 days, the room charges are non-taxable because one entity rented the room. The Department of Revenue policy is not to restrict the 30-day rental to an individual or the same room, but to 30 consecutive days of paid use by any single payor or customer.
etc