A lot of things are going wrong for the Sox right now, but perhaps the most pressing issue is the team's batting average on balls in play (BABIP). According to Fangraphs, the Sox are getting hits on playable balls 22 percent of the time. League average right now is about .285 and, as mentioned by Erik at PHP, the second worst team is more than 30 points ahead of the Sox. This amounts to roughly 25 hits missing over the last 13 games. And given those missing hits, the Sox would likely be an average offense. That is, even if all you did was turn 25 outs into singles, the Sox would have scored in the neighborhood of 20 more runs. That's a run and a half per game.
Ozzie's guys have an average-ish walk rate and are hitting for power above average, but Sox hitters have buried themselves with a lack of regular ol' hits. Obviously, this is bad luck to some degree. A team simply does not hit for a .220 BABIP all season long. Since 2006, no major league team has hit under .278 on the season. But as it turns out, the Sox have been in the running for worst BABIP quite a lot lately:
2007: .278 (Last)
2008: .281 (29th)
2009: .285 (28th)
Is this just a long string of bad BABIP luck then? Well, we can test it statistically to find out. If we know that approximately 68% of teams will fall within 1 standard deviation of the mean given a random normal distribution, then we know there's only a 32% chance a team will fall outside the standard deviation due to pure chance. So the odds that it happens three times due purely to chance is ~(30/100)^3 or 3%. Odds are good that Kenny has been picking up players that simply do not get a lot of hits on balls in play.
This doesn't mean that the Sox are doomed to be anywhere near .220 all season, of course, but it does mean that they could struggle relative to their opponents and may struggle even more obviously in the early going. When runs are at a relative premium as in the colder April/May portion of the season, hits are fewer and hence more valuable. And even once they get going, they'll still likely have to make up a hit or so every other game via walks or HR. So yeah: the clock's ticking on Mark Kotsay.