It turns out that somehow it was ending up on outside the screen and therefore it wasn't being shown on the bottom panel. Here's how to fix:
- Right click on the bottom panel ("task bar" in Windows talk) and select "Preferences".
- Select "Show windows from all workspaces". Then the Firefox button will at least appear on the bottom panel.
- If you can't see the window, right click on its button in the bottom panel and click "Move". Then you can pull the window onto the current display and click again to drop it there.