I'm running MacOS 10.14.6.  I use Sourcetree with remote accounts on both Bitbucket and GitHub.  I recently needed to add a repository from GitHub.  The first problem I noticed was that I could not use the Remote Desktop to clone the repository from GitHub, in spite of carefully entering my GitHub username and password.  It said it couldn't authenticate.  I tried adding my GitHub account in Sourcetree, then retried the clone, but got the same error.  I then used command line git to clone the repo successfully, then opened it in Sourcetree.  After making code changes, I did a push and was prompted for my password along with a checkbox to save the password to the keychain, which I checked.  After that, the push succeeded.  However each time I did a push, I was reprompted for the password each time.  Quitting and restarting Sourcetree didn't help; obviously the password was either not stored in the keychain, or failed to be retrieved from there.

Workaround

A workaround will be added here when available