It seems to be part of his business ethos to be pretty hands off as long as he's not losing money though. I think it was Bryant who pointed out that Kroenke did nothing in the NBA and the MLS too while his teams there crashed and burned.
Other billionaire owners who might only have one or two franchises would probably get more involved during these dips, but I doubt Kroenke has ever watched a full football game. Bloke owns eight or nine other teams in addition to Arsenal. He's looking at it purely as an asset. Along that line of thinking, if Arsenal can grow over a billion in value in a decade where they're nowhere near winning the league, then they can probably add another billion over the next 5-6 years while doing the same thing. It's unlikely that we're going to keep finishing 8th after all. We'll probably ebb out at a level that matches our investment which is closer to a top 5 team.