If I understand it correctly, the amount one tires is pretty much a correlation b/w at bats, position played, and durability. I've kind of got a conservative number (at least for major leaguers) of 6.5xdurabilty to get the number of at bats expected at full rest in a season. He's 85 games into the year, I'll assume he's played all of them, so that's 85 games since the season started. (85/162)(6.5)(91) = 300 at bats, meaning that I'd expect him to be near the tiring point if he had crossed 300 at bats at this point in the season. bighead mentions the 72 spring training at bats, which is a ton of spring training at bats, meaning he was going into the season a little "tired" (though still at 100%), plus being a minor leaguer he didn't have the benifit of the "off days" that a major leaguer sees b/w the end of ST and the start of the real season. You're guy has 315 at bats at this point, plus all the spring training at bats and its not too suprising that he's starting to get worn down.
My formula's a little crude orrdc, but I've got a team w/ a ton of guys w/ low to mid 70s durability, so I move guys around a lot each game and its worked to keep everyone fresh to date (we're closing in on the all star break as well). I'd bet if you sat him for a few days prior to the all star break, and a few days after, then used defensive replacements and/or "rest" replacements he should be fine the 2nd half of the season.