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The Dane, who shot a seven-under round of 63 on the opening day, went round the Gullane course in 77 today, resulting in the 25-year-old missing the cut.
Brooks sits on 11-under for the tournament after a second-round performance of five-under, leaving him three shots clear of a group of six players tied for second, including defending champion Justin Rose and Northern Ireland's Graeme McDowell.
Dutchman Joost Luiten carded the best score of the day, completing his round in a seven-under 63 to jump up 89 places into a tie for 13th on the leaderboard.
Ian Poulter, Colin Montegomerie and Edoardo Molinari were among the other players to miss the cut.