TORONTO — Recent poor performance and bad numbers against J.A. Happ led to a second straight night on the bench for Alex Rodriguez. “He has struggled against Happ,” Joe Girardi said.

The 40-year-old designated hitter entered Tuesday 0-for-14 with three walks and three strikeouts in his career against the Blue Jays lefthander, who was 2-0 with a 1.38 ERA against the Yankees this season.

If A-Rod had been swinging the bat well, Girardi might have had him in there regardless, but that has not been the case. He was 1-for-16 with nine strikeouts since coming off the disabled list, with the hit a two-run homer Friday against the Rays.

“It’s not something where I’m planning not playing him, it’s just he’s struggled against Happ,” Girardi said. “We have not had success against Happ, so I’m trying something a little bit different.”

Before going on the DL, A-Rod had a five-game stretch in which he hit three homers, but overall his season has been rough. Rodriguez brought a .170/.240/.409 slash line into Tuesday, with six homers and 14 RBIs.

Girardi would not say whether he would consider sitting him more frequently if his problems continued. If that happened, it would give more DH days to Carlos Beltran and Mark Teixeira. Beltran was Tuesday night’s DH, which put Rob Refsnyder in rightfield.

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“I’m not really thinking about that now,” Girardi said. “You try to take it day by day in our business, you don’t get too far ahead. But production is important to stay in the lineup.

“If I don’t play him, then everyone’s saying that he’s done, and I don’t necessarily think that. I still think he can be productive.”

Ackley out for season

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Reserve Dustin Ackley will undergo season-ending surgery to repair his torn right labrum Wednesday or Friday. Catcher Austin Romine remains the backup first baseman,

Girardi said, “Right now we’re going with what we have,” but expect the Yankees to explore options outside the organization. Chris Parmelee and Nick Swisher are options at Triple-A.

Gardner’s slide

With Happ on the mound, Aaron Hicks started in leftfield, giving slumping Brett Gardner a night off. Gardner was hitless in his last 20 at-bats and had a .186/.327/.326 slash line in May.

“It looks like he’s pulling off the ball,” Girardi said. “He’s got to make some adjustments, but we’ll get him going.”