I have two problems that seem to be closely related:

• If I log into one site (e.g., English Wikisource), and then open another (e.g., Commons), I am not initially logged in. In some cases, if I reload the page, it turns out I am logged in; but that's rare.
• When I return to the first site (in this example, English Wikisource) I may be logged out.

This happens with surprising regularity, and strongly impacts my ability to do tasks that involve several sites (Wikisource, Wikidata, Commons, Wikipedia, Meta...) This has been the case since the beginning of SUL; I have never filed a bug report before, but when I've mentioned it to Wikimedia tech folks, I get responses that suggest my case may be an anomaly. I don't know that I've ever met anybody who has the same problem.

The issue persists across many browsers and many operating systems.

If it would be helpful, I could make a short screencast video illustrating the problem. (Yes, it's that consistent an issue.)