You put the clause in your agreement about stopping work when invoices are late to protect yourself from being screwed. Smart, that. But what you might not have considered was the client who wouldn’t mind stopping and picking up again when she’s able to pay. What you meant to do was create a disincentive. What your client sees is a way to keep her place in your practice even as she’s not honoring the agreement to pay you on time. She really shouldn’t be able to have both.
To shift this, consider changing your standard to include a consequence to stop this from happening. For instance, it might be that if you have to stop working for non-timely payment more than twice in a six-month period, you’ll stop working with the client all together.