@Mark3179 When you have someone who works for you on a steady basis, does a great job, is dependable and available to clean whenever you need it, be it every 3 days, once a week, or once a month, I think they should be considered as an employee, as opposed to someone you would hire by the hour or job, like a plumber.
As such, they need to be assured of an income they can depend on, like a salary, not that you need to actually pay them a salary. Its like paying someone to be on call should something come up that needs to be dealt with, regardless of whether everything is smooth and they don't need to do anything. Just being available and dependable if needed is worth something.
It's not unreasonable for your cleaner to charge double for month's booking, considering if you had 10 changeovers in high season, she'd earn a lot more.