Thunderbird keeps prompting for google password
There is a problem with the google calendar sync app, and you were recently downgraded to 0.3.2 - you should be at 1.0.2 You can find the correct version at this link, or perhaps by now you can go through the add-on section of Thunderbird to fix this.
If you use the link, you can download the add-on to disk, and in Thunderbirds add-on menu choose install add-on from file. Thunderbird will need to be restarted, but works much better afterwards.