After latest update to SourceTree 2.4.0 and later, it keeps asking for password when connecting on Bitbucket or GitHub while connection on other, privately hosted repos is ok. Previous version 2.3.2 (75) connects without prompting.
Here's what helped (from Atlassian support):
Re-add your Bitbucket/Github account by navigating to SourceTree(Top Nav bar)>Preferences>Accounts(Tabs) using OAuth.
Done that multiple times:
"The request timed out." is the error message
And sometime the error is "Could not authorize request with the available token. Please re-authenticate."
My best guess would be to reach to SourceTree support https://support.atlassian.com/servicedesk/customer/portal/1
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