A lot of homes do not have a properly sized air conditioning system, they are either undersized or oversized. Some homes have 2 units when they could get away with just one. In order to properly size a unit for your home, a manual J heat load calculation must be performed. Unfortunately, a lot of contractors do not perform this calculation. Typically a home in Arizona should be designed to cool around 108 degrees because only 1% of the year does it get above this design temperature.
An oversized unit will go through more cycles in its life than it should and makes it possible for it to suffer a major breakdown early in its life. The more cycles the more likely your unit is to break down because of how much energy has to be drawn for startup. Also those large energy draws from the continual cycling are going to cause you to have high electric bills and it won’t remove humidity well (which can lead to mold issues that can damage your home and is proven to be bad for health). That’s why it’s better to have longer run times and more importantly a properly sized system.
An undersized unit will run constantly because it is not satisfying the thermostat and since it’s not removing enough heat from your home the evaporator coil will freeze. This can cause liquid refrigerant to flood back to the compressor and damage it. If this is a regular problem you will have a compressor breakdown and it will need to be replaced since compressors are hermetically sealed. It is expensive to replace a compressor and is something a professional will have to do.