At a guess, the notifier doesn't know your correct login details:
Right-click the notifier icon that appears on the bottom status bar of firefox, and choose Preferences. (You can also get there by clicking Tools/addons, and then clicking the options button on Gmail notifier).
Check the box "Enable multiple accounts", then click the Accounts button.
Check that your gmail account appears in the list - if not, add it.
If it's there, click on it, and retype your password.
Click OK.
Unless you have multiple accounts, you can now uncheck "Enable multiple accounts".
Click OK