SourceTree can't authenticate with Github

I have SourceTree configured with authentication information for Mercurial on Bitbucket and Git on Bitbucket, GitHub, and visualstudio.com . Recently, SourceTree will not authenticate correctly with GitHub. Although my GitHub credentials are saved in the SourceTree authentication settings, whenever I try to push to or pull from a GitHub repository, a "GitHub Login" window appears and asks me to enter my username and password. Even if I type the information correctly, SourceTree displays an error:

fatal: HttpRequestException encountered.
 An error occurred while sending the request.
remote: Invalid username or password.

However, I can log into GitHub using the same username and password in a browser. If I try to push or pull using the Git terminal, it shows the "GitHub Login" dialog and fails when I enter my information. Then it asks for a username in the terminal, then displays an OpenSSH password prompt. After I enter my password in the OpenSSH prompt, it does connect successfully. However, this approach only works in the terminal, and SourceTree does not detect changes made from the terminal - so if I push or pull, SourceTree doesn't realize it.

I have tried deleting my saved GitHub account information from SourceTree. I can remove GitHub from the sections "Accounts" and "Git Saved Paswords". However, once I remove GitHub from "Git Saved Passwords", it appears under "Rest Saved Passwords" and cannot be removed.

I've tried re-adding GitHub using both OAuth and Basic auth, and in both cases SourceTree reports "Authentication OK" from the settings dialog, but my issue persists - SourceTree always shows me the login prompt when I try to push or pull and always says that I typed in the password incorrectly even when I type it in correctly.

Again, I can log in through the browser or through Git terminal; I haven't forgotten my password and don't have trouble typing it in correctly.