Hello, My name is XXXXX XXXXX X will do my best to help you today.
Your system is more than likely freezing up. This is caused by low refrigerant charge, dirty filter or coil underbelly (the animals would cause this), or the blower isn't running at all. When a system freezes the "A" coil on top of the furnace literally freezes over so the air will not pass through it. Then when you turn the system off it thats and air starts passing through it again.
A good tech can put the gages on the outdoor unit and tell the difference between a low refrigerant charge and a dirty coil.
Cleaning an indoor coil is no easy task and it is not recommended to try without the experience of doing it before. The copper refrigerant lines are very brittle and one false move and you are replacing a coil instead of just cleaning it.