The world number 52 made a costly double-bogey at the par-five seventh, having fired a 68 in the first round, and is one-under for the tournament.
Kiradech is now targeting a high finish over the weekend to get back into the top 50 in the rankings and qualify for next week's WGC event in Memphis.
"Two-over, which is quite a disappointing day," said the 29-year-old.
"Putter was still good, driver, everything was good. It was just the par five, I lost two strokes on par five.
"I'll try to go out there and play my best golf. I think my golf game was much improving. Still with 36 holes for me to climb up on top there, to get myself back in the top 50 again, to get in the World Golf next week."
It is only the second time in six appearances that Kiradech has made the Open cut -- he finished tied-75th last year.
His highest finish at a major was his 15th-placed effort at the 2018 US Open.