Just keep tacking on your late fees. I have bills and late payment due cards that I put in the kids' cubbies. I don't have to say anything -- the parents can see the late fees building everyday, since I make up a new payment due card for each day a payment is overdue.
Whatever system you usually do (bills, email reminders, etc), just make sure she knows everyday how much she owes you. If you haven't reminded her of the late fees that have already accrued, you could say something like "I just wanted to make sure you know that there are $XX worth of late fees on your account so far. If you bring payment tomorrow, there will only be $X more in late fees." You could also give her a call (as others have suggested in other threads), and say "I'm on the way to the bank, can I swing by and pick up that cash?".
I haven't had to refuse care yet, although if the amount outstanding were to get too high, I do have a "discontinuation of care" clause in my policy
