I've seen recent posts on related issues but mine seems to relate solely to login via SourceTree on the Mac. I have version 2.6.3 (134).
I changed my password on bitbucket. That worked fine. But then I could no longer authenticate myself on SourceTree so pushes and pulls all failed. Naturally I quit and restarted SourceTree and checked I could login to bitbucket ok with my new password.
I tried resetting the password in SourceTree -> Preferences -> Accounts but I needed to use my username and not email address (although login to bitbucket is now with email address); then when I changed it to my new password I was not authenticated; the password was changed but then not accepted.
Luckily I did manage to find my old password and reset it in bitbucket and then changed it back in SourceTree (via Preferences -> Accounts) and all is well again.
But if I ever do lose my password I can see the risk of blocking access to all my repositories.