WordPress log out when update css

What theme are you using?

Have you tried:
– deactivating ALL plugins temporarily to see if this resolves the problem. If this works, re-activate them individually (one-by-one) to find the problematic plugin(s). If you can’t get into your admin dashboard, try deactivating via FTP or SFTP or whatever file management application your host provides. If applicable, also remember to deactivate any plugins in the mu-plugins folder. The easiest way is to rename that folder to mu-plugins-old.
– To rule out any theme-specific issue, try switching to the unedited default, core-bundled Theme for a moment using the WP dashboard. If you don’t have access to your admin area, you can switch to the default theme by renaming your current theme’s folder in wp-content/themes and adding “-old” to the end of the folder name using via FTP or SFTP or whatever file management application your host provides. Alternately, you can remove other themes except the default theme. That will force your site to use it.
– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems (because the hooks remain unless plugins completely removed or some plugins stick around in cached files. So by renaming the folder, you break them and force them inactive).
– If the above troubleshooting steps fail to resolve the issue, try manually re-uploading all files and folders EXCEPT the wp-config.php file and the /wp-content/ directory from a fresh download of WordPress. Make sure that you delete the old copies of files & folder before uploading the new ones. Read the Manual Update directions first!

what do you mean by Except /wp-content/ directory.

That’s exactly what it mean – Except /wp-content/ directory.

If you have nothing to lose in that directory, then it’s your choice if want to update it as well.