The former champion had three falls in his last four races over jumps.
Constitution Hill will not run in the Champion Hurdle at next month's Cheltenham Festival.
The nine-year-old made an impressive flat debut at Southwell last Friday.
But after three falls in his last four races over jumps, trainer Nicky Henderson confirmed that the former champion will not be part of the field.
Henderson also confirmed that he will only run on the flat from now on.

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