I checked permissions but another store I’m updating won’t save any editing on the CSS files. All others including admin back end, creating new products, categories, etc works just fine. I’m in the live mode. Not sure what’s going on?
Either put in developer mode or clear cache all the time.
Yeah, mostly likely it’s because you need to clear your cache. Add &cc to your admin panel url… ex: domain.com/admin.php&cc
Also probably need to clear your browser cache for css too. Once it syncs the timestamps, you should be able to make changes without having to do it again.
It looks like it was a caching problem but with Cloudflare on HostGator server. As soon as I turned it off for this site, the update was instant. It was bizarre because with another site running on VPS there were no problems. Such a headache sometimes 
Thank you for all the suggestions!
I guess you can use 'Cloudflare’only with a dedicated IP.