Our company has had very good success by adopting a "before the time" approach. A follow-up call a week to ten days after the invoice has been mailed -- that has a sincerely helpful tone to it, "I'm calling to see if I can be of any help." -- that is conversational and, is full of questions. The longer you wait to make the follow-up call the more touchy the subject may be. And, call every client, every month, without fail...and you will also improve your customer relations.
"Good morning Susan, did you receive our invoice...is everything in order...is there anything else you will need to help in processing our invoice...we are trying to improve our business processes and reduce costs and my part of that is to see what our customers need to improve the payables cycle, does your company shoot for turning payables by the thirty day time window...is there anything we can do to help (mail direct to payables rather than general address, etc.)...I don't want to get in the way so, what kind of follow-up might be helpful?"