I agree. A calm call asking them when you can expect payment can work wonders. See also Len Sklar's "The Check is NOT in the Mail" for how to manage collection starting with your credit policy. http://www.amazon.com/Check-Not-Mail-Without-Customers/dp/09...
Spend $5 and buy a used copy of "The Check is Not In the Mail" http://www.amazon.com/Check-Not-Mail-Without-Customers/dp/09... it will give you a number of suggestions for how to structure an engagement to avoid some of the problems you faced here.
The real warning sign on this was the inability of the company to set a date for a partial payment, telling you to "be patient" instead.