I think there are two issues here, for the technically inclined. First,
how soluble is a gas in rubber tires? Second,
how fast do the gas molecules move through the rubber once it is taken up in the rubber -- that is, what is its diffusivity? These are both functions of the gas's and the polymer's (in this case, rubber) chemical composition, as DMF pointed out, but are fundamentally two different properties. When these two factors are combined, engineers refer to the overall permeability, which is the mass flux (of the gas through the rubber in this case) per unit area per unit time, normalized according to the pressure drop across the rubber.
I did some google searching, and found a paper:
Barrer, R.M. "Permeation, diffusion, and solution of gases in organic polymers." Trans. Farad. Soc. 35 628. It shows that the permeability of argon -- and thus how fast it will leave through the tire rubber, given the same pressure, tire thickness, etc. -- is about three times that of nitrogen. The units for this permeability look a bit goofy, but just take note that the outflow rate would be measured in "moles" or number of molecules, because it is this that determines pressure in the tire.
Some of the replies to this post indicated it might be a waste of time. Don't worry, OP, I think it's an okay question! In fact, I can remember an exam question some time ago regarding patents that Air Products, Inc., (in Allentown, Pa.) had filed for a gas that could be used to pressurize tennis balls. They claimed that the gas increased the usable life of the tennis balls by a factor of two or something like that. I guess I would argue that questions like these, then, can be fruitful/significant!
[EDIT: The tennis ball invention is US Patent 4,358,111.]