I recently made a service call to get my AC looked at cause the fan wasn't spinning. Repair man looked at everything and told me my fan motor was causing the issue and it needed to be replaced, along with the fan blade.

I got that replaced today and I'm still experiencing the same problem. The fan started spinning when I first powered it on and got cold air in the house, but I had to leave to go out of town.

When I came back the air happen to be on at the time because we have it set to AUTO, but the air was no longer cold. Checked outside and sure enough the fan wasn't spinning again. Switched the breaker to turn off the A/C/Furnace and switched it back on, could not get the fan to spin whatsoever and tried different settings, AUTO or CONTINUOUS to no avail. Decided to leave it alone for about 30mins to an hour and tried turning it on again. The fan started to spin and inside the house had cold air through the vents, but not even 10 minutes after, started getting just normal air coming through. The fan once again stopped spinning.

I'm suspecting a bad capacitor, but could it be something else? Any insight on this would help.

I'm suspecting a bad capacitor
It could be but I doubt it.

As far as I know a capacitor works or it doesn't.
Generally AC condenser fan motors are PSC (Permanent Split Capacitors) motors. In other words the start capacitor stay in the circuit. It is not switched out like other types of capacitor start motors.

Clearly the old fan motor was not defective if the problem persist after replacing. You certainly did not need to replace the fan blade.

These things make me doubt the creditability of the repairman. He also makes more money selling you things.

So why would the second fan motor fail? I suggest checking all the electrical connections in the fan wiring. That is unlikely to be the problem because logically the repairman should have remade any faulty wiring connections in the process of replacing the fan, whether he intend to or not.

That leaves the contactor. Obviously the contactor is working if the compressor is working. But burned points in the contactor could be causing a low voltage to the fan motor causing it to over heat and shut down or run slowly.

You can replace the contactor or shut down the power, remove the contactor and examine the points. If you find burned or pitted contact points, replace the contactor or file the points and reinstall. I would file and reinstall.

When the fan motor was replaced the repairman should have replaced the capacitor, too. If he did not then it voids the fan motor warranty, or you have a "jackleg" repairman. I have never seen the main contactor cause the fan motor not to work, but I have seen a relay be bad on the defrost board on a heat pump, or some fans turn off and on with a fan switch which operates on head pressure. The switches can go bad at times. You should invest in a digital or analog multimeter and then you can test things yourself. It's getting harder and harder to get a decent mechanic; you had a "parts changer" instead of a mechanic who did not even have a basic fan blade puller, a necessity to do HVAC work. I bet he did not even check to see if your unit also needed cleaning, a mandatory thing to do when a unit (inside and outside) is over a year old. On a fan motor you have a common (White), a black, and a brown (capacitor) and sometimes a blown and white (capacitor to common). Between the black and white it should read the lowest ohms (10, for example), and from white to brown second highest (60, for example), and from brown to black the total of the two (70, for example), and the brown-white to white it should be zero, since both go to the same point. If the capacitor is the wrong one then the motor is overheating and turning off from the temperature overload in the motor. You can get the correct capacitor within 20% of the required value to correct it before you burn up a new motor. If you have a 10 micro-farad capacitor and it only puts out 5 uF then it will cause the motor to overheat. Any time you have a bad fan motor you can spray a mist of water on the outside coils to cool your house in an emergency, plus this cuts your electricity use in half and makes it cool better when it all works.

Thank you both for your responses.

I called him about the issue and he stopped by the other day to correct it, free of charge. He thought perhaps it could be a faulty fan motor, even though it's new. He put in a new contactor for me also and that seem to have fixed the issue of the fan stopping. Told me if the fan stops again to give me a call so he could get in touch with the fan motor's supplier. Haven't had any issues since, thank goodness.

Any good service technician tests parts with a meter and never, ever just randomly changes parts.