Please provide browser and browser version information, and MediaWiki version information.
Please see https://mediawiki.org/wiki/How_to_report_a_bug for future reference. Thanks!

@Aklapper It is happening on multiple browsers. I tried on most recent versions of Chrome and Mozilla Firefox and it does happen. The wiki farm is Miraheze and it has been reported on multiple Miraheze wikis (https://meta.miraheze.org/wiki/Special:Version). All MediaWiki related settings can be found here: https://github.com/miraheze/mw-config

Does clearing all related web browser cookies help?
Also wondering if capturing the HTTP requests and responses might provide some more info here...

@Aklapper I will try that. I'm not sure how I could get the HTTP requests and responses? If it's a log on a server some of the other sysadmins can get that information.

See info for Firefox ≥24; Internet Explorer; Google Chrome; Apple Safari; Opera

@Aklapper Thank you. I will report once I get the error again (it doesn't always happen).

I've got this error since October or November, and last time some minutes ago at https://meta.wikimedia.org/w/index.php?title=Tech&diff=prev&oldid=16194367. I've got it when rollbacking edits, approving pending changes, and sometimes when I'm trying to save edits to pages. Now I tried to find something from the console, but when I clicked again "rollback", I didn't get the error anymore, and thus could not investigate. So it's not always required to remove the cookies. Sometimes it just works if you try to redo the action later.

I wonder if https://phabricator.wikimedia.org/T147756 is the same, though, they then said the cause was a script, but I doubt.
Was also reported at https://de.wikipedia.org/wiki/Wikipedia:Fragen_zur_Wikipedia/Archiv/2016/Woche_51#Commons and on enwiki, but they are getting this error when trying to log in. I've not got the error while trying to log in, though I very rarely log out.

Do you use Firefox 50.0.1 or newer? Or some different browser?

I have now Firefox 50.1.0. I have always the newest Firefox.

*Edited*

oh nevermind, now this was about loss of session data. will report it there.

That makes me think that this might be again T151770...

In T154241#2907699, @Aklapper wrote:

That makes me think that this might be again T151770...

Yep now I'm pretty sure it's about the same problem. Now I got the both messages at the same time (in different places), first "There seems to be a problem with your login session; this action has been canceled as a precaution against session hijacking. Go back to the previous page, reload that page and then try again" when I tried to revdel a version of one page, then I went to write about these annoying problems to the village pump, and there wanted to save my changes and got the other message: "Sorry! We could not process your edit due to a loss of session data. Please try saving your changes again. If it still does not work, try logging out and logging back in."

I hope that someone can fix these ASAP; I'm not going to change my browser, but getting these every day is horrible.