I kind of stoppped these because it was becoming too depressing but here are the Series Averages now that the time-shifted figures for "The Doctor Falls" are in with the previous few years for comparison.
Series 10 Viewers: 5.64m Audience Share: 27% AI: 83 Chart Position: 20
Series 09 Viewers: 6.16m Audience Share: 25.5% AI: 83 Chart Position: 23
Series 08 Viewers: 7.34m Audience Share: 29% AI: 83 Chart Position: 13
Series 07 Viewers: 8.16m Audience Share: 33% AI: 86 Chart Position: 12
So from Matt Smith's last year to now 30% of the audience has gone and even taking into consideration the ever decreasing ratings for just about everything on television the Audience Share/Chart Position are noticably down. (Though Series 10 is up on Series 9 which would suggest this is a better time of year for the Series to air).
AI has dropped from being consistantly above averge (85) to consistantly below it, though without being able to see the actual audience reports there's no way of knowing if it's because of Capaldi or the scripts or what.
With regard to AI presumably there's something of a fine margin at work given we're talking a handful of points here. I'm just going on what Dr Who TV say
(AI) Audience Appreciation Index is a score out of 100 which is used as an indicator of the public’s appreciation for a show. Over 90 is considered exceptional, 85 or over is excellent, 60 or less is poor, and less than 55 is very poor.
Within those averages there are other stories as well. Series 10 had one episode score 85, which is higher than any in Series 9, and 10's lowest score was 81 for Eaters of Light (which seems a trifle unfair as I kinda liked that one) whereas Series 9 had a 78 for Sleep no more. Pound for pound the consensus of opinion on this board is that 10 is an improvement on 9, certainly more consistent and even though they both average out the same the pattern is different. Obviously this isn't remotely scientific but I knocked this together quickly detailing the AIs of Capaldi's three seasons...

I'd agree that we can't just cite the tail off in viewing figures for the drop in ratings/AI, and whilst I still think the longevity of the show has had some impact, clearly there's an element of Moffat or Capaldi, or possibly Moffat and Capaldi at work. I'm trying to think of another long running show to compare it with. A soap would feel wrong so I guess something like Silent Witness is one of the few things that might compare in the long running dramatic stakes, because what else is there like Who?
Anyway I did have a positive point to make. Even if you take into account the fall in AI/viewing figures, surely from a BBC perspective the show is still healthy. You have a show that's been running (almost) consistently for 12 years and it still draws in 5 million viewers and has AI ratings that are just below excellent. That's a heck of a launchpad for Chibnall and a new Doctor to push on from (hopefully).
If the decline continues, even with a new Doctor and a new show runner then maybe, and I hate to say it, then the problem is just that to the majority of people Who just isn't the vibrant new "we haven't seen anything like this before" show it was back in 2005, maybe to most people it's become old hat, just another show, and either the BBC/fans accept that the halcyon days are gone and live with that, or the Beeb consider it's time for a longer hiatus once more (and I truly hope not!)