She more than likely has diarrhea due to an obsessive amount of protein in her diet. How much protein is in the feed that you are giving her? You generally want to lower the protein and increase the energy amount when feeding grower.
More information about the hen, and your setup is needed for even a reliable suggestion on what may be the problem.
How old is the hen? Where are you located? What is the temperature averaging? What is she being fed? Do you have a picture of the "brown-runny poop"? What breed is she? Where di you acquire her?