So I've saw already a similar ISSUE, but now with 2.x.x versions the app asks credentials frequently...

...and login to github was impossible.

I was trying to delete/restart/re-add user credentials via: Sourcetree > Tools > Options > Authentication - although here the username/pwd was accepted, still no luck with push, sourcetree asked my pwd again and again...
 

Then i've also found this: C:\Users\USERNAME\AppData\Local\Atlassian\SourceTree\accounts.json
Once removing the github related save from here:

1) the push asked me for credentials (new look, big cca. 480x480 dialog) - they've failed
2) then again got a new window for entering credentials (old look, cca. 200x480 dialog) - which succeeded
3) push also succeeded

So this one helped, but the overall user experience is very poor. There's a mess around that authentication and pwd saving.