Does not work with CDN module

I found the same. In this case CDN was serving images from a different domain on the same server.

Same problem. With CDN module configured to serve images images in CSS are no longer embedded.

Same here.

The issue here is two-fold. First, there needs to be a core change; second, this module needs a slight revamp to utilize the hook_file_url_alter() core change.

Its fundamentally a problem with Drupal core (#1961340: CSS aggregation breaks file URL rewriting because it abuses it):

Drupal 7 core's CSS aggregation breaks modules that want to alter file URLs via hook_file_url_alter() because it does not route file URLs of files referenced by aggregated CSS files (e.g. background images, fonts).

From a discussion on the CDN module side (#1532178: Integrate with CSS Embedded Images module).

The solution is for the CSS Embedded Images module to depend on the CDN module and then it will simply have to implement hook_file_url_alter().

Workaround for this exists if using AdvAgg 7.x-2.x
I have a version of CSS Embedded Images that works with AdvAgg 7.x-2.x
Will be releasing the css_emimage code as 7.x-1.3 hopefully sometime soon.
AdvAgg + css_emimage: #1968998: Get a 7.x version out that works with Advagg 7.x-2x

Fixed if using AdvAgg 7.x-2.x & this patch for the CDN module
#1942230-6: CDN module AdvAgg 7.x-2.x Integration