Hello, we are using W3TC with magnification and CDN enabled. The CDN is amazon cloudfront which does not support HTTPS. This problem does not happen all the time but I was just able to reproduce it using safari for some reason.
Essentially the problem is the cached css file has full path links using https to images. Take this for example:
.thumb-control.right{left:auto;right:0;background:url(https://cdn8.site.com/wp-content/themes/mt/img/arrow.png) 0 0 no-repeat}
Since we are on http and cloudfront doesn't work with https this results in broken images. Every image that is used in the CSS file is broken. The only thing I can think of is that somehow the cache file gets saved when the protocol is https thus minifying and converting all assets to https full path links. Then when visiting on http it pulls the cached version which breaks the site. I also am using google mod_pagespeed plugin which may do the actual URL converting if it is not this plugin. Either way, if the css file has to use full path links then 2 css files should be cached one thats loaded on https and the other on http.