Why would tennis balls filled with sulfur hexafluoride explode? An answer at Chemistry.SE tells the following anecdote:

Another fill gas to avoid is sulfur hexafluoride. A tennis ball manufacturer once decided to fill tennis balls with sulfur hexafluoride, assuming this would prevent the balls from going flat as a consequence of the high molar mass of sulfur hexafluoride. But the tennis balls exploded on the shelves because air diffused in.

I understand that the basic reason why this is possible is that concentration difference between the inside of the ball and the outside results in nitrogen or oxygen diffusing into the ball, while the large size of $\mathrm{SF}_6$ molecules prevents their penetration of the ball's wall, so they remain inside.
But why would diffusion lead to seemingly unbounded (until explosion) increase of pressure inside the ball? Shouldn't the internal pressure stop the air molecules getting inside, or at least stimulate their leaving the ball's interior?
Is there any way to intuitively understand this, maybe using some macroscopic phenomenon as an analogy?
 A: As Jon Custer says, this is due to the fact that osmosis balances the partial pressure of nitrogen and oxygen on the outside with the partial pressure of nitrogen and oxygen on the inside. To understand this we have to think in terms of individual molecules, not in terms of overall pressure inside the tennis ball. Pressure is a statistical phenomenon, taking into account behaviour of many molecules. It does not act on individual molecules which only participate in collision processes with other molecules.
Partial pressures balance between the inside and outside of the ball when as many molecules flow in as flow out. The individual molecules have thermal motions according to temperature, unrelated to pressure. So the densities of oxygen and nitrogen, inside and out will equalise. This means that the partial pressures of oxygen and nitrogen, inside and outside, will attain equilibrium, quite independent of the presence of sulfur hexafluoride. Then the total pressure is the sum of the partial pressures of the different gases inside the ball.
Of course this means that if they calculate the correct proportion, they might fill the ball with an appropriate mix of air with sulfur hexafluoride, and achieve a stable balance that way (depending on temperature). I don't know whether this has been tried, or whether it would work given variable air temperatures.
A: 
Is there any way to intuitively understand this ...

Let's look at the number of molecules in a given volume of air or gas inside the ball:
When one $cm^3$ of air outside the ball contains more nitrogen molecules than one $cm^3$ inside the ball, more molecules will have contact with the envelope of the ball outside than inside.
Therefore, more molecules will diffuse into the ball than molecules diffusing out of it.
Diffusion will stop when there is the same number of nitrogen molecules inside the ball as in the same volume of air outside. (Actually, there is still diffusion, but the same number of molecules diffusing into the ball is diffusing out of it.)
The same is true for $SF_6$ and all other gases, so in the end we will have air in the ball with the same composition and pressure as the surrounding air.
However, the probability that a $SF_6$ molecule touching the envelope diffuses is much lower than a nitrogen molecule. Maybe simply because the nitrogen moelcule is smaller.
This means that the nitrogen is diffusing into the ball much faster than the $SF_6$ is diffusing out of it.
For this reason we will have a situation in the meantime when a lot of nitrogen has already diffused into the ball but nearly all $SF_6$ is still in the ball.
In this situation the pressure in the ball is higher than in the initial situation (when only $SF_6$ is in the ball) and it is much higher than in the end of the process (when only air is left in the ball).

... to seemingly unbounded (until explosion) increase of pressure ...

If I didn't make a mistake, the increase of pressure cannot be more than the outside air pressure:
If the outside air pressure is about 1 bar and the initial pressure of the ball was 3 bars, the pressure of the ball will never exceed 4 bars.
This also means: A ball that does not explode when being exposed to a vacuum will also not explode because of this effect.
By the way:
The manufacturer should have filled the ball with a mixture of air and SF6: The amount of air that has the same volume as the ball at normal air pressure should have been mixed with the desired amount of $SF_6$.
In this case the number of air molecules diffusing into the ball is the same as the number of air molecules diffusing out of the ball.
A: 
I understand that the basic reason why this is possible is that concentration difference between the inside of the ball and the outside results in nitrogen or oxygen diffusing into the ball, while the large size of SF$_6$ molecules prevents their penetration of the ball's wall, so they remain inside.

I would prefer to say that the diffusion rates are different (rather than that it is prevented entirely).

Shouldn't the internal pressure stop the air molecules getting inside, or at least stimulate their leaving the ball's interior?


This still doesn't explain it to me intuitively, why the internal pressure doesn't prevent entry of (so many) air molecules.

In the limit of ideal gases, we pretend that the particles are so small that they never bump into each other.  The particles don't know that anyone else is there with them!  Instead we calculate the forces by assuming it just goes back and forth hitting the walls.  The individual particles don't respond to the bulk property of pressure.
In that case, why would the particles leave the high-pressure ball at all if they're not being "squeezed out" by the pressure?  Purely chance.  If the temperature inside the ball and outside are the same, then we presume they're moving at the same speed. Also, any holes are symmetric (it's just as easy to get in as get out).  In that case the diffusion rate depends only on the number of particles bouncing around the holes.  In the high pressure ball, there's a lot more bouncing near the hole and in the low pressure ball there are fewer.
Given the symmetry of the hole, if the (partial) pressure of the substance inside is higher, more on the inside will strike near the hole than will from the outside.  Over time, this will tend to decrease the quantity remaining.  They're not being squeezed out, they're randomly bumping into a hole and leaving and not being replaced as quickly.
