Imagine a bottomless ball pit, just to clarify, it means a bottomless pit filled with uniform hollow balls. From "experimentation" I know that there is still airflow at the bottom of a 0.5 meter tall ball pit. I assume that this is because air can still flow in the gaps between the balls.
But in a bottomless pit, can there be a situation where there will be no available pass for air to reach a certain depth. Also, related, can there be a case of not total lack of air, but reduced air flow to the point of not allowing human life at a certain depth (not enough new oxygen will come to replace the CO2 released by the human).
So in other words, in a bottomless pit filled with uniform spheres, is there a depth where all routes for the air to reach will be cut off? If not, assuming that at a certain depth $h$ there is $f$ air-flow, is there a depth where the available airflow will be $f_0 << f$? (Not sure how to mathematically properly define "airflow").
The standard ball size is (according to Wikipedia) is
no larger than 3 inches (7.6 cm) in diameter
Since the kissing number of spheres is 12, and spheres can only touch at a point, I'd say that there always exists a path for the air to take, no matter the depth, i.e. a packing of sphere's won't be airtight.
In terms of airflow, I guess that depends on how it's defined, but I think I'd be worried about the weight in balls crushing me before I worried about running out of air.