Mike, please include to the mailing list as well, so others can help you out too. Why do you need the trigger to be FOR EACH STATEMENT? so I can understand your use case, even if it's simple stuff, please share with us your code.
Oh, so you're defining transition relations (REFERENCING NEW TABLE, OLD TABLE ) as in here?
CREATE TRIGGER paired_items_update AFTER UPDATE ON paired_items REFERENCING NEW TABLE AS newtab OLD TABLE AS oldtab FOR EACH ROW EXECUTE FUNCTION check_matching_pairs();