Just out of interest I wonder if it might be worth checking what CBeebies is doing flag wise? It presumably still shares its playout with BBC Four so if the flag issues are with the equipment at "their" end, the same should happen on CBeebies. In theory. I'm presuming they still share equipment and there isn't a physical change to other hardware after CBeebies goes off the air.
I'm not 100% sure but I believe the playout for CBeebies and BBC Four are no longer shared. The BBC channels moved to a new transmission suite last year, built on a more modern infrastructure including IP video, and I believe they took that opportunity to split the playout for all the services.
There's been a number of special occasions over the last few years (i.e Olympic games) where the broadcast hours for the kids channels and BBC Four (and Three before it ceased broadcasting) have overlapped, which caused a few headaches given that they normally shared playout. So I believe they decided to run them all separate to avoid any potential future issues, especially given how easy it is to setup multiple services with modern playout solutions.