Kapur, who shot an even round of 72 on the first day, was even par for the first eight holes before running into a double bogey that put him in danger of missing the cut.
Another bogey on 12th almost ended his chances, before he hauled himself back with back to back birdies on 14th and 15th followed by an eagle on par-5 17th.
However, a closing bogey on par-4 18th again put him on the line with a total of one-over 145 for 36 holes.
The clubhouse leader was Rafa Cabrera-Bello with identical rounds of 69 in the first two rounds and he shared the spot with Richard Green (68-70).