Gmail - POP or IMAP ?

If POP, have you selected to use 'less secure apps' via the gmail webmail account?

If IMAP: In Account Settings, Server settings, are you using 'authentication method:' OAuth2'  ?

re Pop-up - select 'allow'. This pop up is probably occuring because you keep having to logon. When i set up gmail it also asked me, but only the once because I've only been asked once.

As of version 38 Thunderbird uses OAuth2 for authentication of Gmail accounts. This is the only way considered 'secure' by Google. http://techcrunch.com/2012/09/17/google-oauth-2-0-for-gmail-and-talk/

Basically you authenticate with your Gmail account password once, and you have to allow Thunderbird to access your Gmail account. Google then provides you with an authentication token. This is what Thunderbird saves as 'password'. It's not your actual Gmail password. The token will expire at some point, so you'll have to renew it in the future. Make sure to have Thunderbird remember the 'password', otherwise it will prompt you again and again.

Thanks for the help I'm using imap and the OAuth2 authentication. Actually I wondered why the "saved password" was not my password but that makes sense now..

It is set to remember passwords and does work on my laptop but for some reason on my desktop it would still prompt me for it each time and I don't see a check box for the Gmail login to save the password.

Try to clear the 'password' Thunderbird has remembered. It will then prompt you again the next time it's needed. Make sure to check the box to remember it then.

Also see http://kb.mozillazine.org/Setting_and_changing_email_passwords

Thanks I will give that a try and see if that fixes it.

On a kind of related topic, do you know if there anything that give a little more details on how (well) it encrypts your passwords when you use a master password?

This will give you an idea. The same goes for Thunderbird. Beyond that, Google is your friend. http://security.stackexchange.com/questions/48174/if-i-use-a-good-master-password-in-firefox-is-security-improved-when-i-remember

When your problem has been fixed can you mark the thread as 'Solved' please? Thank you.

Thank you, christ1, for both the info about 0Auth2 AND the reminder to click the box to have my pw remembered. That was key. What I can't figure out is why I just started having this issue with the authentication token this week, after using Tbird for years.