Kapur, who was lying 45th after the first round seemed to be on his way to making the weekend rounds following an eagle on the ninth at which point he was one-under for the day and one-over for the tournament.
But four bogeys on the back-nine, including three in a row from 14th to 16th, almost put him out of the tournament. He made it on the cutline at four-over and in the 65th place. 81 players made the cut at five-over 147.
Korean Sihwan Kim, who failed to pick any of the four berths from the five-way play-off at the US Open qualifiers, seemed to be making up by taking the halfway lead.
Playing his first season in Europe, Kim shot a two-under 69 in the second round to lead at six-under.
Joint overnight leaders Adam Gee and Simon Wakefield carded 72s to sit at three-under, two shots behind second placed South African Darren Fichardt (69).
The 500,000 euro tournament is co-sanctioned by The European Tour and the Challenge Tour, and the prize money counts for both The Race to Dubai and the Challenge Tour Rankings. The winner will gain a European Tour exemption until the end of 2013.