Why did Tiger's golf skills disappear for so long?

There are many reasons.

Off the field distractions with the highly publicized divorce and womanizing.

His cyclical time frame for a self imposed swing change. A player of his dominance is always demanding of himself for improvement. The time his divorce surfaced publically was the beginning of his disdain for his then current swing. He switched to a new swing coach in the last few years. This is similar to tearing a house down and building a completely new one. From there he has worked tirelessly to commit this new swing to muscle memory, which leads to confidence in practice, to confidence in tournaments, which ultimately leads to confidence in major championship which his career accomplishments are based on.

He has had numerous operations on his left knee. This can also cast doubt on a swing as the fear of injury is present with each viscous swing he takes. Quite possibley his conscious or subconscious concern for his left knee then lead to other injuries in his neck and back over the last few years as well. Each injury delays practice and playing time for him to gain prescoius confidence in his new swing.

Not as important but still a factor is the level of play around him. There are several supremely talented golfers competing against Tiger now compared to 1997-2008. Add to that his aura of dominance lessened during his travails. There was a perceived mental advantage Tiger held over his opponents resulting from his historic career. Players realized he too is flesh and blood and was beatable. Possibly most important in this change was his loss at the 2009 PGA Championship after holding the 54 hole lead. Something he had never done before.