I am using the latest version of Sourcetree desktop (version 2.4.8.0), and it keeps asking me for GitHub authentication. No matter what I enter there (username, email, password, github generated token), it keeps popping again. Note that I am able to authenticate to my Github account successfully through web, so that's not a spelling issue. I have also contacted the Hithub support already, they have advised to upgrade to the latest version of Sourcetree and then contact you if it doesn't help.
Do you have any ideas what's causing this and how it can be fixed