oEmbed stopped working for new posts

Hi,

I have a peculiar problem, ‘all of a sudden’ oEmbed, which we mainly use for youtube links, stopped working on our website for newly made posts, or older posts that we edit.

Thus an old post like: https://nieuws.thepostonline.nl/2013/10/31/video-filmmaker-geweerd-vara-zwarte-piet-debat/ still works with just the YT link in the text: oEmbed works nicely.

But a test post I’ve edited later on, doesn’t have the proper embed codes generated by WP anymore: https://www.thepostonline.nl/2013/10/28/nieuwe-mazda3/

We’re running on nginx, WP 3.7.1, but no problems thus far.
The only thing that I can think of is that we’ve started using Cloudflare this weekend, but I don’t see how that could impact anything like thise.

Does anyone else have any clues?