There are a few reasons why your A/C may stop blowing chilly air after a while. One reason could be that the refrigerant in the system is not being circulated properly. The refrigerant is responsible for absorbing heat from the air inside the room and then releasing it outside. The refrigerant that has combined with impurities will not be able to absorb the heat from the air inside the room and the A/C will stop blowing chilly air. Another reason could be that the A/C filter is dirty and needs to be replaced. A dirty filter can restrict airflow and cause the A/C to overheat. Lastly, the A/C may simply need to be serviced by a professional.