In the past few weeks I've been running the A/C pretty consistently. The house will cool down and then periodically will start to warm up again slowly. I checked the inside unit - fan still blowing but just cool air - and outside unit - not running.

If I flip the breaker for the furnace off and then turn it back on, everything starts up again, i.e. furnace fan and outside unit, and house cools down again as normal. Seems to be happening every 24 hours or so.

What could cause the outside unit to stop like that?

Veryoften there are pressure switches which sense the pressure of the refigerant. When it gets warmer and/or there is some restriction of air flow around the condenser the compressor will shut down on "high head" meaning high head pressure. Depending on the age of the equipment it could be a simple as cleaning the coil. But in some instances the condenser fan motor will overheat and quit, causing the high head pressure. At any rate... check the condition of the coils. Pollen, dust and other airborn contaminates can plug the outside coil making it more difficult for the fan to extract heat to keep the pressures inline. Does the unit seem to quit after seveal hours, or just at the hottest part of the day?

I've noticed it in the latter part of the afternoon, for the most part, with one or two exceptions. It has been in the 90s or so lately so it's been running a good bit.

Once I flip the breaker, everything comes back on and works as normal. I just had my annual service a month or so ago and they said it was all systems go. Is this something they wouldn't catch in an annual service check?

Not sure if this makes a difference but on the Thermostat the fan was set to Auto. I turned it to just "On".

Also, just now I could hear the outside unit starting up on its own again (after the house cooled off it shut itself off for a bit). Now all systems are working.

Of course this isn't to say that it won't shut off again later only to have the house get warm again.

If it was cool during the systems check it's possible that this situation wouldn't be discovered. When I had HVAC people check our facility for startup, there would always be a call back on a hot day when the equipment reacts differently. Leaving the fan on will certainly help circulate the room, and mopst likely delay the situation you are describing.