Over the span of May and June, Preston Claiborne had a 1.46 ERA, 3.39 FIP and opponents OPS'd a mere .554 against him. That great start to his season kept his numbers up as a league-average pitcher, however, the rest of the season was a different story. Between July and September, he had a 6.66 ERA, 6.38 FIP and opponents OPS'd .889 against him, so either hitters figured him out or something went wrong. It was probably a combination of the two.
As the season went on, Claiborne lost velocity on all his pitches, other than his changeup. In the first half he average 93 mph, but in the second half he was down to 92.1 mph. That 0.9 mph difference is the biggest seen in a Yankees reliever, other than David Robertson, who lost 1.1 mph on his fastball and was shut down toward the end of the season due to shoulder fatigue. The only other Yankee to experience a similar decrease in velocity was Boone Logan, who eventually missed time due to an elbow injury.
When Claiborne's velocity dropped, he lost the ability to get hitter to chase out of the zone. In the first half of the season, batters swung 37.9% of the time at pitches out of the strike zone. In the second half it fell to only 31%. With hitters swinging at less balls his contact rate on balls outside the zone plummeted, going from 75.7% to 58.2%. Normally, avoiding contact is a good thing, but getting hitters to swing at balls out of the strike zone will either lead to swinging strikes or weak contact. Now Claiborne was no longer able to fool hitters and everyone just laid off the stuff he was throwing outside the zone and waited on the pitches he was still throwing over the plate. Instead of weak contact, he was now getting a plethora of fly balls (33.7 FB% vs. 41.5 FB%) and, obviously, a lot more home runs (14.3 HR/FB% vs. 18.5 HR/FB%). After posting a 1.52 BB/9 in the first half, his 3.92 BB/9 in the second half couldn't support him anymore.
As a result of his inability to get batters out, his fastball value fell from a slightly bad -0.49 fastball runs per 100 pitches to a legitimately bad -1.87. His slider was even worse, going from a positive value of 1.86 all the way down to -2.25. His change up was his only valuable pitch all year, though it still lost value in the second half, going from an outstanding 5.58 to a still good 2.18.
It was pretty clear that he wasn't very effective anymore and the Yankees knew it. They sent him to the minors toward the end of the season and he pitched sparingly in September.
In the end, he could have been tired. For the last two seasons he's generally pitched to the same pitches per inning rate (16.8 pitches per inning in 2013, 16.1 pitches per inning in 2012). In the first half of this season he pitched to an elevated rate of 17.23 pitches per inning, which is understandable since he's facing major league hitting. By the second half he was at a heightened 20.7 pitches per inning while only throwing one inning more. He might have pitched at the same rate over the season, but the heightened rate toward the end definitely didn't help him maintain his strength as the season wore on.
Maybe that's a good thing; fatigue is a lot easier to combat than ineffectiveness.