I'd like to offer some commentary "from the other side of the story," i.e. I am someone who is in the trajectory of losing his fastball at age 74, which is nearly nine years into my retirement. First, there is nothing intrinsically wrong about losing mental acuity, but there is a responsibility that one must assume, namely to ensure that any damage to others will be minimized, or even fully offset if you can do it. I was fortunate in my career, as I always had surrounded myself with talent different from and greater than my own, so it worked out well that the more I trusted the people around me, the better our whole organization became. In the case at hand of our beloved Head Coach, it is harder to make the case that his Assistants have been better (retired Coach Scar may be the most shining example of a "better" Assistant, but the track record of Belichick's "tree" has not been impressive). It's a great risk to have Steve B. in his post, as the chances of a son correcting his father are less than a non-family member being able to fix an issue.
Second, the hardest moments of the "losing fastball syndrome" occur when you're still sharp enough to know that it's happening, and others haven't yet caught on or are just starting to catch on. In my own case, I have always had cheerful memories of the collie next door when I was 14-16 years old; I never had a pet-anything and this dog was such a mood-lifter. But this past weekend, I agonized for most of the weekend trying to remember the dog's name until "Cindy" finally jumped into my head from out of nowhere last night. I see how important/central it is to Belichick to be able to "go down memory lane" on arcane topics such as the evolution of long-snappers. I suspect that he may be trying to prove to himself that he's still "with it." Also, a tried and true way to throw people off the trail that you're losing your fastball is to be in control of what will be the subject matter of the conversation.
Third, there is a balance between remembering the lessons of history (as "there is nothing new under the sun," so new problems are often old problems wearing new clothing) and not being able "to go with the times." It may very well be true that what was a mistake earlier (going for it on fourth and two, with the pass to Faulk not getting the needing yardage) is today's correct call (the contemporary analytics smile on going for it on short fourth-down yardage, especially when your defense is gassed). Still, it is just too easy to conflate bad decisions with bad outcomes. I'm blessed that in my own life the worst decision (based upon a weighted-criteria approach) which was to get married at age 21 turned out to give me the best outcome 52 years later (being in the same marriage, with two kids and their kids having all turned out to be wonderful and still connected with me). Perhaps professional athletes are different now than when Belichick learned the trade under Parcells, and it would have been better to let up on the "Johnny from Foxboro High" harangue upon Brady after he had won whatever number of Super Bowls.
Finally, success can each go a long way towards buying time. The Patriots so far this season remind me of one of my favorite Milton Berle lines ("I have sex almost every day - I almost have sex on Monday, I almost have sex on Tuesday, etc."). Indeed the Patriots have won almost every game so far this season. I suspect that in the next few weeks, perhaps stirred most by the return of Trent Brown if/when it happens, will start to have more "moral loss" (I think the terminology was introduced upthread) moments, and we'll even be tempted to believe that the genius mind has found its way home to our Coach.