Do you have the Downloads folder in the Library?

What does the about:downloads page show? --- Firefox manages downloads in the Downloads folder in the Library (History -> Show All History)

• downloads are treated as history items: clearing history removes included download items and vice versa.
• the Download button gets a blue highlight once all downloads are finished to make you aware that new downloads are available.
• Pause and Resume can be found in the right-click context menu of an item.

• https://support.mozilla.org/en-US/kb/Downloads+window

I'm having this problem, too. I checked about:downloads and there's a huge list of things I've downloaded, but the downloads don't appear in the library, only All Bookmarks.

You can check for problems with the places.sqlite database (bookmarks and history) in the Firefox profile folder.

• use "Verify Integrity" on the "Help -> Troubleshooting Information" (about:support) page
• https://addons.mozilla.org/firefox/addon/places-maintenance/

See also:

• http://kb.mozillazine.org/Locked_or_damaged_places.sqlite
• https://support.mozilla.org/en-US/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file

If "Verify Integrity" on the "Help -> Troubleshooting Information" (about:support) page or Places Maintenance can't repair the places.sqlite database then remove all places.sqlite file(s) in the Firefox profile folder to make Firefox rebuild the places.sqlite database from the most recent JSON backup in the bookmarkbackups folder.

• keep a backup copy of places.sqlite in case a new places.sqlite database has to be created
• http://kb.mozillazine.org/Unable_to_process_the_backup_file_-_Firefox

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox