The research floor works a bit differently than other treatment rooms. Instead of a treatment timer running down, the patient will need to be treated with a specified number of medications - they won't be done until they have received all of the required medicine.
Medicine for the research floor for the research floor - medical bags, propeller hats & DNA - ais obtained by completing emergency operations. So that means providing the emergency vehicles (ambulances, helicopter & Co.) with the needed items until you've completed them (see the progress bar at the bottom of their windows).
Fully healing a patient on the research floor will grant you access to new diseases!