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Many digital thermostats have programmable fan timing for off-delay timing to slightly increase efficiency (fan stays on for pre-determined time after A/C shuts off) but the thermostat should have nothing to do with what you are describing.
You may have a problem with your A/C, Especially if it is happening more often.

One thing to check is if the thermostat has a time delay built in for compressor safety. If your unit has a built in time delay, it will add to the thermostat time delay and the unit may not come on for 10 minutes or so.
If the thermostat has a time delay, you can usually program it so it has no time delay. Try that and if that doesn't work, you may need service.