I have a digital thermostat and recently my AC hasn't been running correctly. I have been keeping the thermostat at 76 and the AC maintains that temperature. However, if I try to lower it to 74, it will cool to 74 and then continue to run but always shows 74. The only way to get it to stop running is to raise it again. I have been trying to research this and have found very little. The only thing that resembles this at all is a blower relay problem. Any ideas or suggestions are welcome!

*I have changed the digital thermostat batteries*

When you lower to 74 and when 74 is reached, does it continue you blow cold air/does the condenser outside keep running?
Or is it just the inside blower that's running?

When set at 76... does it cycle on and off?. as you would normally expect... when set at 74 but fails to stop running... it sounds like the system may be having trouble dealing with the extreme summer heat... i.e... system too small for size of the house, house insulation inadequate,. or it could be a component failure as you suspected. One thing I always check is the performance of the unit... get a good, accurate thermometer and measure the temp of the air at the intake grille (usually where you find the filter)... then measure the temp at one of the air outlets... if the system is operating properly and the system is appropriately sized for the house... you should see about a 15 degree difference between the two... NOTE... there are many factors... this is a basic diagnostic test.

Another issue can be that some of the ducts (attic, crawl space, etc.) have become loose and/or unattached.

Or... the ducts in the attic are not properly insulated...

The list goes on and on...

when you lower to 74 and when 74 is reached,,does it continue you blow cold air/does the condenser outside keep running?
or is it just the inside blower thats running?

It does continue to blow cold air, but the thermostat never goes below 74. I checked and the outside unit is still running.

When set at 76.... does it cycle on and off ? .... as you would normally expect .... when set at 74 but fails to stop running.... it sounds like the system may be having trouble dealing with the extreme summer heat.... ie... system too small for size of the house, house insulation inadequate, .... or it could be a component failure as you suspected. One thing I always check is the performance of the unit.... get a good, accurate thermometer and measure the temp of the air at the intake grille (usually where you find the filter)... then measure the temp at one of the air outlets.... if the system is operating properly and the system is appropriately sized for the house.... you should see about a 15 degree difference between the two.... NOTE... there are many factors ... this is a basic diagnostic test.

Another issue can be that some of the ducts (attic, crawl space, etc.) have become loose and/or unattached.

or.... the ducts in the attic are not properly insulated...

the list goes on and on ......

It does cycle on and off on its own at 76. However, it seems to take longer than it should (or used to take). I only have digital thermometers so I can't do the temp thing at the moment.

Any type thermometer that's accurate is OK .

A genuine refrigeration thermometer is not too expensive and will prove handy for other applications later. The inexpensive ones that have an 'ice pick' type of point can be pushed through ducts, etc. really handy and cheap... I keep one of them in the a/c vent duct outlet in my truck... if the temp there gets below 32 it tells me the freon is low. The temp there should be about 38- 42... if the temp gets below 32 it makes ice on the evap coil and blocks the air flow. Feels great till the air stops !