You gave us a link with all his stats and no context; in fact, most of them showed consistency.
Why in the hell are you using icorsi? Do you even know what that is, and why most people look at overall corsi or corsi rel? THAT is your metric for his decline?
I'm sorry, you're getting ridiculous. Using icorsi instead of just about every other commonly accepted measure of player value is literally looking for reasons to dislike someone/cheapen their performance. I can do that for almost any player in the league, if you wish. Especially given that you think less goals/more assists is bad.
iCorsi is probably a very useful stat in this case. It isn't perfect, because CF60 is also very useful to see how effective a player is at generating shots for his line as a whole. Kopitar has been very consistent for the last 5 years or so, he's always right around 60 for CF60, and always one of the top on the team in that category. That's pretty damn good.
This is what's concerning though:
iCorsi/60
07-08 - 11.3
08-09 - 14.6
09-10 - 14.3
10-11 - 14.5
11-12 - 13.8
12-13 - 11
13-14 - 12
14-15 - 9.8
15-16 - 8.2
The biggest problem with this lack of generating shots for himself is this:
Points/60
07-08 - 1.67
08-09 - 1.88
09-10 - 1.76
10-11 - 2.69
11-12 - 2.07
12-13 - 2.04
13-14 - 1.95
14-15 - 1.83
15-16 - 1.12
His production trends the same as his iCorsi fairly closely, which is heading the wrong way and has been for a few years. Kopitar is a great passer, but he's dominant when he's generating shots. That's what the team needs from him.
Kopitar is deferring more and more to his teammates, despite absolutely knowing he needs to shoot more. In my opinion, he's too unselfish. He is so freakin good defensively that he can easily take more risks and still be a selke type guy.
It should also be noted that even though Kopitar is playmaking more than ever, his Assists/60 is abysmal so far this year at .37. His worst previous year was .88, and the rest .99 and above. Small sample size and all, but still alarming. It should normalize a little, but if he has his typical mid-year slump it's a problem.
I'm not as concerned with giving Kopitar an 8 year contract as some, he absolutely needs to be re-signed. It might sound ludicrous now, but if trends continue he's going to be a $9M+ defensive specialist in 4-5 years time. I'm fine with that, as the windows going to be closed, but there isn't a single metric that points towards his production leveling out - it's all trending down. That's expected, but the rate is concerning.
I don't think it's a physical thing either, I think it's completely between the ears. If someone can get him to get back to a shoot first kind of guy, he could easily be near a ppg for the next 4 or so seasons without sacrificing his defense.
It's fun analyzing players and their worth, but it's likely all moot as he's going to sign for 8 years and the team will sink or swim with him going forward.