The air conditioner fan may be at fault for causing the fan to run throughout the cooling cycle. It could be something as simple as a dirty fan blade preventing the unit from shutting off. Check the fan setting and see if it's under 'auto' mode instead of 'on' to allow cooling.
There could also be other internal issues within the unit, such as a malfunctioning thermostat. Other components, such as the condenser and evaporating coils, could be at fault.
It's best to call a professional when all interventions have been exhausted. The air conditioner may require further evaluation for maintenance or repairs.