Occasionally problems develop with the places database which stores your bookmarks and history, and problems also can develop in the settings file which stores your toolbar configuration. But the more common issue is a conflict with an extension.

Could you try Firefox's Safe Mode? That's a standard diagnostic tool to bypass interference by extensions (and some custom settings). More info: Diagnose Firefox issues using Troubleshoot Mode.

You can restart Firefox in Safe Mode using

Help > Restart with Add-ons Disabled

In the dialog, click "Start in Safe Mode" (not Reset)

Do the buttons work in Safe Mode?

Problems with bookmarks and history not working properly can be caused by a corrupted places.sqlite database file.

You can check for problems with the places.sqlite database file in the Firefox profile folder.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox
• https://support.mozilla.org/kb/Bookmarks+not+saved#w_fix-the-bookmarks-file