DIAGNOSIS The plastic carafe base (the handle part the glass sits in) has warped from repeated heat exposure, or the small metal tab on the warming plate that depresses the brew switch is bent.
FIX First, inspect the warming plate. There's a small, round, silver switch in the center. Ensure the metal actuator tab directly above it isn't bent downward. Gently bend it upward slightly with pliers if it is. This is the most common fix.
IF THAT DIDN'T WORK The carafe base itself is warped. The only solution is to replace the entire carafe. You must get the official Elite Gourmet EHC4128 carafe, as the shape of the base and the placement of the trigger nub are specific.
HEADS UP Never place a cold, wet carafe on a hot warming plate. The thermal shock can crack the glass and also warp the plastic base. Always ensure the base is dry before placing it on the heater.