My Gmail Notifier Firefox add-on had stop working for several months already, and apparently the Offline Gmail feature from Gmail Labs is the culprit.
Updating to the latest version of Gmail Notifier (0.6.3.11 at the time of writing) didn’t help at all, but fortunately this can be fixed by simply installing this: hosted2.xpi
It works for me, [...]

Gmail has been my primary email client for years already—for its simplicity, effectiveness and speed. With the new incoming feature in Gmail Labs, namely Offline Gmail, Google had successfully stopped me from bothering to look at any alternatives.

Gmail is no doubt one of the best free email service provider out there, but as Nick Vujicic says in one of his speech:

the day you believe you’ve reached your fullest potential is the day you have not. (2:31)
Thereby, the Gmail engineers are always looking for ways to improve Gmail, and one way is to [...]