Why do unused tires lose their pressure? I have two tires, and I filled both with air at the same pressure. I used one for one month and kept the other one unused. 
Surprisingly, at the end of first month I found that the first tire had more pressure than second. Why is this so?  
 A: My guess is that the pressure difference you observe is caused by other factors, rather than a tire being used or not. 
Most probably by heat. 
When you drive your car your tires get heated up. When exposed to sunlight, they get heated up again. 
Given the (approximately) steady volume of the air inside the tire, temperature increase would result in pressure increase. 
You can check the table at wikipedia; for example going from $24^oC$ to $38^oC$ could increase pressure by 5%.

You should repeat the "experiment" after letting the tires you used cool down for several hours or a day. Ensure they have the same temperature and measure their pressure again. 
A: One cause of pressure loss in tires is permeation of air molecules right through the rubber, as gas inside the tire tends toward equalizing pressure with the outside.  This will happen regardless of whether a tire is in use or being stored.
But when a tire is in use, frequently rotating under load and at speed, a great deal of external air pressure is created in the area of contact between tread and road, when air is compressed into the tread grooves and between the tire and the road.
It's conceivable that external air pressure between road and tire while the tire is being used, drives air molecules through the rubber, from outside to inside, and compensates for the slow permeation of molecules out of the tire while it is stationary.  A tire in storage doesn't benefit from external air pressure caused by road contact.
The quality of rubber, of self-sealing puncture material, and the design of the various layers of the tire may vary sufficiently from manufacturer to manufacturer to affect how easily gas permeates through the tire.  Higher quality tires may not deflate as fast as low quality tires in storage.
A: My speculation is that the weight of the car stays on one segment of the wheel sufficiently long for the rubber/steel at the bead to distort or creep and therefore lose air. If the wheel is rotating the force is distributed evenly around the bead.
A: This is not really a hard question...it's just that the proper assumptions haven't been enumerated!
You have two tires. Purchased from the same lot, identical in every respect that matters.
First Assumption: Tires are mounted identically, on identical rims, prepared identically, with identical UNLOADED inflation pressure.
Second Assumption: The tires are mounted TRADITIONALLY, which is to say that they are dry-seated against the rim, or perhaps with a grease, and the only thing actually holding the tire to the rim is the 36psi inflation pressure, which is enough to seal the rubber against the rim.
Third Assumption: The rubber is malleable, and distorts/forms to the minute imperfections of the rim.
Fourth Assumption: The tire-in-use is supporting 1/4 of a vehicle.  The tire-in-spare is supporting the cloth/naugahide cover in the vehicle's trunk.
Fifth Assumption: The vehicle is being driven on well-maintained roads, with minimal sharp, high-velocity changes in tire shape/pressure.
Result:  the mounted/driven tire will, under the load of the vehicle, have slightly higher pressure.  This pressure will hold the otherwise dry bead of the tire tighter in its mounting groove.  The more you push on the tire, the more it resists losing pressure from its seal. The quiescent tire however, being at slightly lower pressure, will allow air to leak, especially when the ambient temperature drops, and the rubber stiffens, and particularly when the inside-the-tire temperature is lower than the outside air temp.  This is the other factor:  tires in use heat up, even if only by a bit.  Race car tires can heat up quite a lot...hyundai excel tires, not quite so much.  but SOME.
A: Rubber is, to some degree, porous but it's more likely that most air is escaping at the bead of the tyre, where it's in contact with the wheel rim.   There will be some relative movement between the tyre and rim as the two rotate, the tyre deforms, and the seal is compromised.   That would explain why the stored tyre doesn't lose so much air (anyone who has ever owned a bicycle with tubed tyres might recall the tendency of the tyre to creep around the rim).
Air loss is also exacerbated with alloy wheels - the alloy is often slightly porous and the wheel rim has to be lacquered at regular intervals to maintain the seal.
