There's a lot of functionality that that check is looking for, not just that the jfbconnect.js file exists. On your page, the Facebook Javascript library is also missing. It should be present right after the opening body tag. It's a big block that's configured a little differently for each site. The main line the Autotune tool looks for is:
js.src = "//connect.facebook.net/en_GB/sdk.js";
That's not present on your site which means:
a) The plugin isn't enabled
b) Some caching is preventing the plugin from altering the page output
c) There's some other conflict with your system (uncommon)
I'd recommend disabling JCH entirely and anything else that may be altering the output. Then, run the checks again and re-enable things until it fails to localize the issue.
I hope that helps,
Alex
Plugin FAIL when doing 'AutoTune'
