Eventually the mixture will reach an equlibrium state where the energy released from the reaction will raise the temperature to a point that the reverse reaction (reformation of H2 and O2) is as fast as the forward reaction.

That temperature is easy enough to find. It's the adiabatic flame temperature for H2 and O2; about 3080K

http://en.wikipedia.org/wiki/Adiabatic_flame_temperatureIn principle the whole lot might revert to the starting material but the odds are against it.

Calculating thr real probablity isn't easy so in the great tradition of such things I will calculate them for something simpler.

Imagine a box with a sliding partition down the middle with nitrogen on one side (left) and argon on the other. They are at NPT and just to make thigs easier we can pretend the N2 molecules have the same weight as the Ar (theyr'e pretty close and itf you aren't happy with that we can put the box in orbit so they are weightless).

Then you take the partition away and wait.

After a while the gases mix. How likely are they to "unmix"?

Well, their positions are decided by chance and the chance of any one atom being in, say , the left hand side is 50%. Consider each atom or molecule in turn.

There's a 50% chance that the first nitrogen is in the left hand side. There's a 50% chance that the second nitrogen is too so ther's a 1 in 4 chance they both are. look at a 3rd nitrogen and you have 1 in 8. Keep playing this game for all the molecules in the box. For the sort of size of box you might carry groceries in there will be about 10^23 nitrogen molecules. That means the likelihood of them all being on one side of the box is about 1 in 2^(10^23)

We are talking about pretty thin odds here. A google years doesn't come close.

In case you wondered, I hadn't forgotten about the argon. The likelihood of them all being on the right side of the box is pretty much the same number so the probablity of both things happening is roughly the square of that probablity

I think that's about 1 in 2^(2*(10^23))

OK that's a very rough aproximation to the original question but the odds are so remote that if I'm out by a hundred orders of magnitude, it barely matters. I'd need to know what the box was made of but tunneling might be important. The suposed half life for the decay of protons ( something like 10^35 years) would certainly be a factor.