For recurring invoices, Payment Center provides a way to rollover unpaid balances to the latest invoice. This feature is fully documented here: Revolving Balance.

To have a recurring invoice exempted from balance rollovers, first expose the following flag in the recurring invoice layout, then check the flag to carry out the exemption: Screen Shot 2013-10-24 at 11.03.16 PM

 

This feature is available in the October 2013 release.