Running headers will not reset to blank when used with multiple stories.
Create a multi-page document, and flow some text into. Create two paragraph styles (Section # and a Section header). Create a running header using both with a page number (P [Section #:] [Section header]) on the master page.

Now, if you add a new section # and a Section header a couple pages in, the footer will update. If you put a blank Section # paragraph, the section number will disappear from the footer (as it should). Now, if you start a new the story on a new page and put a blank Section # paragraph and a Section Header style at the beginning of the new story, the Section header in the running footer will update, but the section # will stay the same as the previous story. It will not blank out. It should behave the same as when there is a single story in use. This is a bug that has been forcing me to manually edit my footers for some time. I would really like it to be fixed.