It is possible that there is a problem with the file(s) that store the extensions registry.

Delete the files extensions.* (e.g. extensions.sqlite, extensions.ini, extensions.cache) and compatibility.ini in the Firefox profile folder to reset the extensions registry.

• https://support.mozilla.org/kb/Profiles

New files will be created when required.

See "Corrupt extension files":

• http://kb.mozillazine.org/Unable_to_install_themes_or_extensions
• https://support.mozilla.org/kb/Unable+to+install+add-ons

If you see disabled, not compatible, extensions in "Tools > Add-ons > Extensions" then click the Tools button at the left side of the Search Bar (or click the "Find Updates" button in older Firefox versions) to check if there is a compatibility update available.

If this hasn't helped then also try to delete the addons.sqlite file.

You can check for problems with preferences and try to rename or delete the prefs.js file and possible numbered prefs-##.js files and a possible user.js file to reset all prefs to the default values.

• http://kb.mozillazine.org/Preferences_not_saved
• http://kb.mozillazine.org/Resetting_preferences

I attempted this several times, deleting more of the files you recommended each time. The problem persists, unfortunately.

Create a new profile as a test to check if your current profile is causing the problems.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer some files from an existing profile to the new profile, but be careful not to copy corrupted files.

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

Thank you, that worked perfectly.