I was having a similar problem where the Blubrry PowerPress player was not appearing when I was using WP Super Cache.
I discovered a fix and I'm adding it here.
If you're using WP Super Cache with a CDN, such as CloudFront (or the CDN Sync Tool), then on the CDN Tab in WP Super Cache ( /wp-admin/options-general.php?page=wpsupercache&tab=cdn), you will need to exclude .swf files form the CDN / Couldfront Cache.
Exclude if substring: .php, .swf
This excludes the /wp-content/plugins/powerpress/FlowPlayerClassic.swf file from the CDN, which is necessary for security purposes. There may be a more elegant fix to this issue, but I found it just as easy to not include the .swf files; and I didn't test this, but I bet there's a cross domain scripting error if you try to pull the .swf from cloud front.