I use WPengine and have the same issue when copying from live site to staging. I have to manually copy and paste the ccs from the live site to the staging site.
It seems as if this plugin is hardly supported anymore.
The host (Hostmonster) said that it was an issue with the w3 total cache plugin. I disabled the plugin and the formatting returned. The plugin has always worked fine with my website. Not sure what happened or if the issue is related to Hostmonster.