With the report of unlimited private repos on GitHub, I decided to give it a shot. I created a couple of private repos. Then I connected my GitHub account into SourceTree. And I am not able to view any of the existing repos in GitHub. I am running the SourceTree Beta, if that makes any difference.
I have searched through the community forum, as well as the KB and online. I found some articles but nothing that helped to allow me to see the repos.
I haven't uninstalled and reinstalled SourceTree but that seems a bit extreme. SourceTree is able to connect to GitHub.
When you open Sourcetree and click on remote, do you see anything? As an example I'm attaching a screenshot of my Sourcetree where you can see Bitbucket pinned on top:
Can you also share a screenshot of yours?
If you try to clone a repo from your Github account by clicking on New > Clone from URL do you get any error?
Let us know!