A room that stays cold is a common complaint, and it does not always point to the equipment. Often the cause is in the ducts, the registers, or the way the house is set up. Sort those causes first. Then decide whether the system's age belongs in the picture.
Check the pattern
Note which rooms are cold and when. If every room sits below the set point, the system is short on output or the thermostat is set low. If only some rooms are cold, the cause is more likely in the distribution. If the cold rooms are the ones farthest from the unit, the duct run is the likely reason.
Check the supply and return
With the system running, hold your hand at each supply register in the cold room. Air should be moving clearly. Weak or missing airflow points to a closed damper, a blocked register, a kinked flexible duct, or a crushed run. Check the return grille too. A blocked return can starve the whole system and make every room feel weak. Check the filter at the same time, because a loaded filter reduces airflow everywhere.
Check the house
Look at the doors. A closed interior door on a room that has a supply but no return can trap warm air. Look at the insulation in the room's exterior walls, the ceiling above it, and the floor below it. Look for gaps around windows and outlets on exterior walls. These do not show up on the thermostat, but they change how much heat the room holds.
When the question is the equipment
If airflow is good in every room and the system still cannot reach the set point, the question moves to the unit. Ask the service provider to measure the temperature rise across the unit, check the refrigerant or fuel side, and confirm the system is running at its rated output. Ask them to explain each result in writing.
Once you know which side the problem sits on, use the guide for your system to read its age. The central air conditioner, heat pump, and gas furnace pages each give typical service life and planning notes. A cold room is a reason to look closely. It is not a reason to assume the system is at the end of its life.