Final answer:
A mid-latitude cyclone dissipates during its occlusion stage when the cold front catches up to the warm front, cutting off the warm air that fuels the system.
Step-by-step explanation:
A mid-latitude cyclone begins to dissipate at its occlusion stage. This happens when the cold front catches up to the warm front, cutting off the warm air from the surface and thus eliminating the cyclone's main energy source. The cyclone becomes 'occluded' as colder air encircles and traps the warm air aloft. Without an influx of warm, moist air to fuel it, the cyclone loses its strength and eventually dissipates. Furthermore, when the cyclone moves over land or cooler ocean water, the reduced temperature differential and increased friction also lead to the weakening and eventual dissipation of the system.