How often is too often to ask the same relative to babysit?

It's release season at work, I'm often there till 9 or later, and my partner's hospital shifts don't bend. My aunt lives fifteen minutes away and always says yes when I ask her to take our daughter for the evening. That's the problem. I've asked four times this month and I can't tell anymore if she's happy to do it or too polite to say no. How do you keep this fair? Do you pay family, cook for them, set yourself a limit?