It's all invoices. But, here's what's really strange.
When I say "all invoices", there are only two past due invoices. That's because we don't have very many invoices to begin with, anyway.
So, I troubleshooted this by manually pulling these two invoices through Process...Apply Entries. Afterward, I deleted these two records from Payment Journals.
Then, I went back into Payment Journals, used Suggest Vendor Payments, and it worked!
My "revised question", therefore, is why is Suggest Vendor Payments working only for invoices that are manually pulled in to Payment Journals first?
John