Complex sentence: Henry VI (1422-61 and 1470-71) closed the bath houses due to their bad reputation as fronts for brothels, but demand for bathing was so great he was forced to reopen them, limiting the number to 12.
Split into simpler sentences: Henry VI (1422-61 and 1470-71), due the bad reputation of bath houses as fronts for brothels, closed them down. But demand for bathing was so great he was forced to reopen them, limiting the number to 12.