24-hour day cares often cater to health care workers, and they pay a premium price for the flexibility.
My college daughter is headed to a career as a nurse, and if she works in a hospital (as opposed to a doctor's office), she'll likely be assigned to work three days a week x 12 hour shifts. This is something that she kicked around a great deal before she decided this is the career for her.
I've told her that if she remains in this area, we'll offer her the same deal my grandmother offered us: We'll babysit while you work, and the money you would've paid to day care will go into a college account for the child. My grandmother believed very, very strongly in education, and this was a win-win for everyone.
Something I have heard my fellow teachers say frequently: "Since I've paid for it 'til 5:00 anyway, I'm letting my kids stay in daycare an extra hour today so I can run my errands. What takes me 30 minutes on my own takes two hours with the kids." I think this is a pretty good choice. Toddlers don't enjoy being dragged in and out of their car seats for various errands.