You re probably closing individual windows, instead you need to close down Firefox from the menu.

Firefox Menu Button {Three bar icon) -> Close (or Quit) {Standby icon)

Note that you can check via History > Recently Closed Tabs/Windows to see if you can restore closed windows (the maximum default is three windows).

This happens whenever FF is closed down, by any method, including restart, when the computer jams, when I've left the browsers open on the desktop. When one of two browser windows reappears, and not the other, is there ANYTHING I can DO to re-create the other browser, without opening some of the URLs manually via History?

You can try the Session Manager extension.

• https://addons.mozilla.org/firefox/addon/session-manager/