The simplest approach is automatic reminders tied to the date the vendor committed to, sent a set number of days before the due date and again on the day. Relying on someone to remember to chase a vendor is exactly how pending items turn into overdue ones.
The reminder should say exactly what is due and link straight to where the vendor can submit it, which makes it easy to act on. If the date passes without a submission, the status should change and the right internal person should be notified so they can decide what happens next.