They some criteria.
1) without payment method assign in invoice also we can run for APP. but condition what ever we are giving credentials in APP it must suitable. Example invoice must come under in Next payment run date is most important then only system will pick up.
2) After proposal created u can check in edit proposal and if u will get invoices in edit proposal means your settings is correct and working fine but problem is u can cross check why it is comming in error message.
3) chceck manually in FBL1N vendor any open items are there and u can check the fields in document
4) for other vendors APP working fine and a particular vendor app is not working means there is no change in FBZP settings and u have only look invoice and already any proposal also executed for that vendor.