It's interesting watching videos of him from four or five years ago on youtube versus what we see now. He's lost something, I'm not sure if it's explosiveness or athleticism but I think it's pretty evident. I do doubt it's ever coming back though.
I wonder at times if he became too complacent as a top level shot stopper and failed to devote any serious training to the parts of his game in which he's always been lacking. To be fair to him, I doubt the churn of Managers and goalkeeping coaches hasn't helped him develop either.
I would imagine there are ways of testing his physical reaction speed, so you'd think the club would know if that was the issue.
From the analysis I've seen, the problem largely seems to be a combination technical inaccuracies that weren't in his came previously, concentration errors and then confidence errors. Which suggests to me your second paragraph might be more accurate. A combination of losing focus, coaches who allowed faults to continue/develop in his game (his penalty technique being the prime example) and then the self-doubt that then naturally comes when things start going wrong on the biggest stage (thinking of that World Cup in particular).
It also looks like as he tries to solve one issue in his game, others appeared. So for example he has largely cut out the concentration errors this season and improved his sweeping but then his shot-stopping seems to have declined. Whereas in prior seasons his shot-stopping was still hitting top heights more regularly but concentration errors were screwing him over.
More so than any physical decline, to me he's looked like someone who is stuck inside his own head over the last few seasons.