You're right, they could be showing signs of financial trouble -- or they could just be busy / lazy / inattentive to your invoices, which happens often enough in accounts payable departments.

I don't think this alone is enough to warrant cutting ties with a client, but there are a few things you can do.

1. Amend your agreement to charge % interest on invoices after some grace period. This will incentivize on-time payment.

2. Amend your agreement with them to require a personal guaranty, i.e. if the company doesn't pay, the signer is personally liable for the sum owed. I've been told this is an easy judgment to win in court, which means you hopefully won't have to go to court.

3. Let them know that after 21 days you will cease services until their balance is paid.

4. Have an earnest chat with the head of the company. S/he will pass the message along to accounting.

I hope this helps. Let me know if you've tried any of these avenues...