I disagree with an answer saying that tires normally lose 1-2 psi pressure per month. Yes, the upper limit (2 psi) can be okay, but the lower limit (1 psi) is definitely not correct.
Where I live, tires need to be swapped twice per year, as winter tires are mandatory during the winter. Typically, when I filled a tire to 2.3 bar for my 2011 Toyota Yaris when installing it, a year later (when it has been half a year in service and half a year in storage) the pressure is typically something like 1.9 bar. This is a difference of 0.4 bar, or 0.03 bar per month. In psi, it is approximately 0.5 psi per month.
The tires in an older 1989 Opel Vectra seemed to hold pressure much better: often times, when installing the tires (or actually the wheels), the pressure was correct and the tires needed no inflation. Based on this, the lower limit is indeed much, much lower than even 0.5 psi per month. However, once one winter tire had lost considerable amount of pressure during a year, but the remaining three had correct pressure. I don't know what caused this but the problem didn't repeat.
So, I would say that tires normally lose 0.1-2 psi pressure per month. I suspect the ultimate lower limit is caused by diffusion of air through the rubber. Nitrogen diffuses slower than oxygen, so nitrogen holds up pressure better. Remember, however, that about 80% of air is nitrogen. The possible 2 psi per month pressure losing is probably caused by a seal between the wheel and the tire that isn't completely airtight. If this seal is bad, I suspect nitrogen won't help at all.
Interestingly, bicycle tires lose pressure much faster, and high-pressure tires need to be filled approximately twice per month. I suspect this is caused by the fact that bicycle tires have less rubber so the air can diffuse through the rubber easily. Also the fact that bicycle tires have only part of the rubber (the inner tube) as an airtight seal probably plays a major role in this.