I am using SourceTree v2.6.9.0 on Windows 10. My repositories are in Bitbucket, and my Bitbucket account has 2-step verification.
For several days, maybe about a month, SourceTree has started showing a dialog asking me for my Bitbucket login, about every 20 minutes or so.

This is the dialog that I get. The difference is that it has the username pre-filled.
It doesn't matter if I enter my credentials, or simply close the dialog without doing anything, the dialog keeps popping up several times a day. And also, I can keep pushing and pulling without issues, even if I just simply ignored the dialog and closed it.
Other people in my office, with the same version of SourceTree, and accessing the same repositories in the same way, don't get these. The one difference between them and me is that I have been using SourceTree for about a year, or more, while everyone else started using it, on my recommendation, in the last couple of days. This has made me think that a fresh install would solve my issue, but I am not convinced. There should be a better solution.
I've tried solutions like this one https://community.atlassian.com/t5/Sourcetree-questions/SourceTree-continuously-prompting-for-colleague-s-BitBucket/qaq-p/601906
without complete success. After following the instructions on that answer, I don't get the login dialog every 20 minutes, but now every 2 hours and 40 minutes (yes, I write the time every time I get the popup).
I am not sure what else to do, apart from uninstalling, and re-installing SourceTree.