I'm not sure, honestly. I've never seen an issue like that before. It seems to be some sort of Javascript collision that's preventing the Facebook's Javascript library from either detecting the finish of the page load or calling it's routine which parses out the Facebook 'tags' into the actual widgets (Like, Follow, etc).
Looking at the code, the following Javascript file is being loaded on your page:
com_didww/assets/javascripts/didww_common.js
In that file, the Facebook Javascript library is being re-loaded. My guess is that, depending on how the page renders, that re-loading is causing the conflict and sometimes working and sometimes not.
Is there any way to disable that file, or social features, within the com_didww component? If not, I can help you to comment out the Facebook Javascript loading in that file and test from there, which should work.
Thanks,
Alex