Mark Teixeira's 2010 was arguably his worst offensive season since his rookie year in Texas. He had a career low BABIP (.268), however his 19% line drive rate was essentially unchanged from his previous 4 year average. He did have a higher IF/FB% last year compared to his average (17% to 12%), which does include line drives. Maybe Teixeira was lining out to infielders more often last year, I really don't recall.
I took a closer look at Teixeira's line drives and found that he was hitting fewer liners on balls up in the zone. Compare his line drive rate graphics for the last 3 years:
Teixeira's overall BABIPs over that same time period: .346, .302, .268. If his LD% hadn't take a 5% dive, I'd be more willing to believe he was just having bad luck with high pitches. Pitches hit up in the zone tend to end up in the air more often than on the ground. There's a chance that Teixeira was hitting more infield flies on pitches up last season (I don't have any data on zone specific IF/FB% at the moment).
The shift is often deployed against Teixeira which might skew his LD%. Plays that are technically "ground outs" when the ball hits the outfield grass first on a line and then gets fielded by an infielder on a shift would otherwise get labeled as a line drive if there was no shift and the ball got through for a hit. We're working with a small sample size when isolating one portion of the zone, so it's possible just a few of those kinds of outs could have brought down his LD%. I guess an interesting study would be to see if players that see shifts have lower line drive rates in addition to having fewer ground ball hits.
As it stands, it doesn't look like Teixeira was unlucky on high pitches last year; he didn't have his best season at the plate and hitting fewer liners off pitches up in the zone was probably one reason why.