I'm having the same problem - I have a mixture of Pi1 B+ and PI2 machines all running LibreElec 7.0.2 and none of them will play CBeebies HD. I thought at first that it was something to do with the retune that happened recently but it seems to run fine on a Kodi instance running on Windows 7. My backend is running MythTv 0.27 and I'm using TBS cards to grab from Freesat so I thought perhaps there was an issue with the PVR addon, however I tried creating a short recording of CBeebies HD and again it runs fine on Kodi on Windows 7 but won't run on any of my PIs. The file also seems to run fine on VLC on windows so it doesn't look like there's anything particularly wrong with the file itself.
When I get a chance I'm going to try to grab some logs and other info. My 3yr old hasn't noticed that he's watching CBeebies in SD yet..