Which line(s) pose Black problem(s) in the King's Indian defense on the highest level of competition? King's Indian defense is rarely seen in the highest level these days.
Queen's gambit declined took over for now.
I am trying to find out if there are any lines that put so much pressure on Black that top GMs decide not to play it.
GM Vassilios Kotronias has written a detailed series of books covering more or less every system that white can try against the KID. In the final volume of his series, he notes four systems as the most dangerous ones at white's disposal. These are:

Mar del Plata
Makogonov
Gligoric
Sämisch

As someone who has played the KID for most of my chess career so far, I can only say that Kotronias' assessment is more or less spot on (which shouldn't come as a surprise to anyone who has read his series on the KID). The main lines in these systems are truly nasty.
Edit: after rereading the question I wish to give a perspective on why top GMs refrain from using the KID. I don't believe the KID is an unsound opening, and from a theoretical perspective there is no specific line that causes black too much headache to deal with. The problem with the KID is that it carries serious risk for black, regardless of its theoretical status. Black will often need to &quot;trust the engine&quot; and enter dangerous and sharp lines in order not to fall into a horrible position (just look at what Grischuk had to do in the 2013 candidates tournament when he played the KID against Svidler - the line he played looks like the work of a mad man, but is in fact the only real way for black to maintain equality after 12.f4). While this risky play is fun, it is not always viable for a top GM. When you play the KID as black you cannot force a calm game, and for professionals who need reliable openings that they can play when they need at least a draw the risk that the KID carries is simply not acceptable.