It doesn't really make any sense to argue that these guys aren't capable. Especially not these guys. Sure, maybe Gordon Beckham's confidence is so shot that he's hit the last walk-off hit in his life. It's unlikely, but it's still a more arguable point than claiming that Alex Rios (owner of a walk-off HR this season), CQ (owner of a walkoff HR in '08), and Konerko (King of '05 Playoffs) aren't capable of producing in the clutch.
The South-Siders just haven't gotten lucky in the land of 10,000 lakes and 10,000 balls caught at the warning track. (Unless you count Friday night, where they won despite allowing a 6-run inning and scored a run when Alex Burnett fell over and balked rather that throw a pitch)
The White Sox have had a great deal of 'showing their mettle' games of recent. Contests where the team has looked out of it or defeated, only to rally to make a game of things in 'garbage time', and lose when their efforts fall just short. As much pride and hope that Ozzie, Hawk, and other mildly unhinged figures obsessed with the team manage to take from games that still count as losses, I can't help but wonder if there could be any effects of the team buckling in the 9th with the chance to win in grasp...repeatedly
If closers can become ruined mentally after having their guts ripped out in the 9th too many times (I wish MLB had available video so I could splice in clips of Fausto Carmona's body language in '06, whereas I'm glad they have no video coverage for everything that happened to Donnie Moore after the '86 ALCS), why wouldn't the same issues occur on the offensive side? Confidence at the plate and the change it brings is apparent in watching the difference in Gordon Beckham this season, Paul Konerko in 2003, and Brett Lillibridge of the past month and a half compared to any other point in his big league career.
The problem with reading into these late game performances is that baseball is a random game. Well, not so much random as prone to a great deal of variation; which is why such efforts have been made to cull the statistical norms from the game. God forbid some young kid goes to Target Field, sees Nick Punto hit a home run, and fails to grasp that they just saw something Judy Garland-level crazy. (Worse yet, what if a young White Sox fan in 2003 saw Billy Koch go through an inning without walking someone?!?!?) One of the reasons that the season is 162 games long, besides shameless profiteering, is so it can properly draw out meaningful results.
One of the few benefits of the White Sox team being unevenly packed with old fogies is that they should be emotionally mature enough to handle this sort of stomach-punching, game-ruining, division-race altering failure.
Still, this team didn't really turn their psyche around until they started winning, which is what the Sox need to do to maintain their positive feelings about the season. As much one would like to think that a team that won 25 of 30 games to close the first half would have a mental advantage over a Twins squad missing two of their best players and having spent the last few weeks watching their lead crumble, that just isn't the case.
On the whole, this team has already been through too much this season to be discouraged by a string of 4 games (June 27th vs. Cubs, June 30th vs. Royals, July 16th vs. Twins, July 17th vs. Twins) where they've blown opportunities to win the game at the plate. This team is still not that great at hitting, so perhaps short of Mark Teahen fielding a grounder, these are the worst gotta-have-it moments the Sox could be placed in, and not a good test of their ability to play in the clutch. And as we all know, it'll just take one big hit to produce dozens of "This team never says die" quotes. It'd just be nice if it could come against the Twins.