Update:
Did a bit more testing. It seems to present when using a Chrome browser, but not Safari or Firefox, even with multiple tabs logged into different public Galaxy servers (.org + .eu).
I’d suggest switching to using Safari or Firefox to avoid the logout problem.
Not sure yet exactly what is going on with Chrome, but am in contact with the developers about it for follow-up. Clearing the browser cache doesn’t seem to resolve the problem.
I’ll also contact the GTN – we might want to add that advice to the tutorials that include a “Get Data > UCSC main” step. Most likely that would belong in the FAQ associated with the tutorial until resolved (might be resolvable on our side – or it might be a UCSC session issue, and we can contact them about it once the root issue is isolated).
Hope that helps for now!! 
Related Q&A: Output of UCSE table browser get data creates a new history and logs the user out. - #3 by jennaj
We’ve noticed this occurring at sporadic times when pulling data in from the UCSC Table Browser for about a year. We couldn’t isolate why at usegalaxy.org.
The advice from @Flow may work (and is a good idea anyway): one tab open to Galaxy at a time.
If that doesn’t work (are still getting logged out), then after pulling the data from UCSC, log into your account. Datasets can be copied/moved between histories as needed.
This doesn’t happen very often, and it has only been reproducible for short time windows in the past at usegalaxy.org. I’m not sure about usegalaxy.eu, but both use the same underlying Galaxy version.
I’ll run this by the development team again.
Thanks for reporting the problem!