The answer to 'why is my shut-off valve slow draining' is that the valve may be partially clogged or corroded, preventing proper water flow. This can happen over time as sediment and mineral buildup accumulate in the valve. Symptoms include slow or reduced water flow when the valve is turned on.
To fix a slow-draining shut-off valve, you may be able to try DIY solutions like turning the valve back and forth to dislodge debris, or using a valve key to open and close it several times. However, if the valve is severely corroded or the problem persists, it's best to call a professional plumber to inspect and potentially replace the valve.