As of version 2015.3 Telerik TS extensions are signed by Firefox in order to be installable.
You may try delete the extension, enable it again and restart the browser.
Firefox extensions could be installed manually, as shown below:
- For installing the playback extension navigate to: C:\Program Files (x86)\Telerik\Test Studio\Browser Extensions\Firefox4+ and drag telerik_test_studio_automation-2015.2.918.0-fx-windows.xpi to the extensions in FF.
- For installing the recording extension navigate to: C:\Program Files (x86)\Telerik\Test Studio\Bin\TestRecorderBrowserExtensions\Firefox and drag telerik_test_studio_recorder-2015.3.1228.0-fx-windows.xpi to the extensions in FF.
Let me know if that helps.