Does the tire lose air when it doesn't have the air cap thing? Someone stole the cap from one of the tires.

 

No, the tire won't lose air just because the cap is off. However...
The cap keeps dirt and crud from getting into the valve and possibly causing it to
stick open while you're checking pressures or adding air, which will can the air out.

 

I think that's what is happening already. Better go buy one then.

 

Put a little soapy water in the tip of the stem, you'll see very quickly if it's leaking air through the valve.
Be careful doing this if it's really cold out, you could freeze up the valve.
If you do find that the valve is leaking, it's not hard to take the valve core out and clean or replace it - you dont have to take the tire off the car.
If the valve is leaking it won't stop just because you put on another cap. G/L.