J.
I don't think that frequency of time off is acceptable, regardless of whether it's paid or not. At the rate she's going, that's about 20 days a year!
If you really like everything else about her, it's time for a meeting where you clearly and briefly tell her what you need and ask her if she thinks she is able to do that or not. Something like: "in order for us to continue to keep our jobs, we need to have childcare that is reliable. That means, unless it's an emergency, no more than about 1 personal day off every two months, and personal days need to be scheduled a week in advance at least half the time. We like the care you are giving our children, but this isn't an optional choice for us, it's something we have to do in order to meet our job responsibilities." And then give her the option to think about whether that's a commitment she can make to you.
If not, I'd look for another nanny. Also, you might see if there is anyone in your neighborhood who has a home daycare where they will take an occasional extra child. We have an arrangement like that with a couple of local home daycares, who have helped us out when our home dcp is closed for vacation.