It seems to be cache issue.
Open your CSS file in browser. Please do Ctrl-F5 to force a cache refresh.
F5 may give you the same page even if the content is changed, because it may load the page from cache. Ctrl-F5 forces a cache refresh, and will guarantee that if the content is changed, you will get the new content. What requests do browsers' “F5” and “Ctrl + F5” refreshes generate..
If it is updating the modified dates, it sounds like it is working but is merely a browser cache issue. Have you tried doing a hard refresh and/or clearing your browser cache or trying in a private browser tab?
Doing this should resolve the issues you are facing.