Cold Rydberg atoms provide long coherence times and strongly enhanced electric-dipole moments, but many cold-atom microwave electrometry schemes rely on cyclic preparation and probing sequences that reduce the measurement duty cycle. We demonstrate microwave electric-field measurement based on magneto-optical trap (MOT) fluorescence-loss spectroscopy in a continuously operated cold ^87\mathrmRb ensemble. A 780\; \mathrmnm probe beam and a 480\; \mathrmnm coupling beam drive a two-photon transition to the 46\mathrmD Rydberg states. When the two-photon resonance is reached, atoms are transferred out of the MOT cooling and fluorescence cycle, producing a measurable decrease in the MOT fluorescence and enabling real-time optical readout without switching off the trap. By optimizing the probe and coupling laser powers, we obtain a fluorescence-loss linewidth of about 6\; \mathrmMHz, close to the linewidth limit mainly set by the natural linewidth of the 5\mathrmP_3/2 intermediate state and approximately one third of the linewidth reported in previous cold-atom fluorescence-loss microwave measurements. With a resonant microwave field coupling the 46\mathrmD_3/2 and 47\mathrmP_1/2 Rydberg states, the loss spectrum exhibits Autler-Townes splitting, and the extracted splitting increases linearly with the microwave electric-field amplitude. For detuned microwave fields, the measured peak separation follows the detuned Autler-Townes relation, providing a route to infer microwave detuning under calibrated conditions. These results show that MOT fluorescence-loss spectroscopy can preserve the low-Doppler environment of cold atoms while retaining continuous operation and real-time fluorescence readout, offering an experimentally simple pathway toward continuous cold-atom Rydberg microwave sensors.