Something is slightly marginal - it will show up on HD channels first as they need better signal quality. As the content on BBC News HD is no more edifying than BBC News SD and you get the channel in good weather you could elect to live with it.
I’d expect the other channels in the same multiplex to be affected - BBC One Scotland HD, BBC One Wales HD, BBC Scotland HD, BBC Four HD and Cbeebies HD.
A 60cm dish “should” be OK in 86 - you are just in/on the edge of the UK spot-beam footprint for 60cm. I have a 60cm dish in 56 which is normally fine- but I think we did lose some channels when we had absolutely torrential rain the last time we were over.
It’s possible that the installation pre-dates the re-focussing of the UK spot-beam (my memory says 2012 but I can’t find a reference for the moment) which had the effect of improving reception in the UK (and northern France) at the expense of southern France (well, it is a UK spot-beam) so the dish was probably fine at the time that it was installed.
If you want guaranteed uninterrupted viewing on all channels then check everything is aligned perfectly and that you have good quality coax, well made connections and maybe a new LNB (water can get in though that usually causes total failure). You could explore a 75cm or 80cm dish as well if you want but that might be overkill.
PS/Edit: BTW the transponder shown in your pic - 10714 - is Channel4/E4/More4+1/Film4, if you can get your box to show it the signal quality & strength for 11023H would be more use as that’s the one giving you problems (but they might be perfectly OK now the weather has cleared).