This is a very good question! I have been desperately wondering about this myself for a long time. I've recently read an interview with his father-in-law and coach, Arshak Petrosian, who gives some insight: https://chess24.com/en/read/news/petrosian-on-talent-character-and-near-misses
And here's another interview, this time with Leko himself, about a 9 month (!) break he took from chess: http://www.chessintranslation.com/2011/08/leko-explains-his-break-from-chess/
But even after reading these I don't feel satisfied. Seriously, what on earth happened to Peter Leko?
Leko drew a title match in 2004, and around then also won all the big super tournaments (Linares, Wijk, Dortmund). A dozen years ago many would guess that Leko today would be World Champion or at least top five. He was born four years after Kramnik and Topalov, who both have been ranked #2 behind Carlsen fairly recently. But what happened?
In April 2003 Leko was 4th on the rating list, with the ten years older Anand just ahead on 3rd, but today Leko is more than 100 Elo behind Anand. In October 2008 Leko was still top 10 while Nigel Short was #85. Short was then 43 years old and Leko still in his 20s. Today Short is 52 years old and 15 places ahead...
In Biel Leko won his first game against an opponent in the 2400s, but it wasn't too impressive. His opponent spent too much time trying to find a way to win, and then blundered on the last move before the time control. Round 2 was back to "normal", with Leko making mistakes in the middlegame to lose against Ponomariov (who also has fallen out of the 2700 club).
At another site the question on what happened was answered with that he got married, but he married 17 years ago, long before his best results. And contrary to Kramnik, Anand, Kasparov, Radjabov, Topalov, Grischuk, Karjakin, Giri, Svidler etc he doesn't have any kids, so in that respect he has an "advantage" in that he can spend even more time on chess. But as he has been playing the last decade it is easy to forget how close he was to become World Champion.