We use an air popper to make popcorn at home, and there are always a few unpopped kernels at the bottom. Far less than for microwave popcorn, and not enough to worry about waste-wise, but a few. I became curious about whether these were just unpopped, or actually unpoppable.
Verdict in my N=1 experiment: Yes, almost all of them can be repopped! The easiest thing is to just toss 'em back in the popper for next time. Throw 'em back, they're not big enough yet. ;-)
It took several months to collect enough unpopped kernels to do this experiment. Eventually I had 48 g of kernels, about 1/4 cup. When I started the popper, I noticed that the air coming out smelled slightly of burnt popcorn. The flakes (the puffs are apparently called flakes, unless Wikipedia is pulling my leg) were smaller and denser than usual, and had a very high percentage of mushroom shapes, rather than butterfly. I suspect these are signs of reduced popping force. The surface on the mushrooms mostly had a fine-grained texture of light brown, rather than the larger speckles I'm used to seeing. The flavor was fine, though there was a little tendency towards the flavor of puffed rice.
Afterwards, the flakes weighed in at 43 g, and the remaining intact kernels at 3 g. (That scale was only accurate to about a gram, and there's some water loss in popping.) Only 6% of the kernels, by mass, did not pop.
I also noted that the air popper did not fully empty when I first ran it. An annular wall of popped and unpopped kernels 5 cm high and 1 cm thick built up inside the popping cavity, and I had to dislodge it by shaking. I don't have a solid explanation for this, but I suspect that the reduced vigor of the popping failed to mix and clear the chamber as effectively as it is supposed to. This may or may not represent a fire hazard, but I would bet it would have quickly led to Burnt Popcorn Smell. So: Not only is collecting the unpopped kernels for months to pop in one batch a waste of time, it's counterproductive. But it's entirely reasonable to leave them in the popper for next time, and just get rid of the ones that turn dark brown. (Oh, and probably don't put them back if they have salt and such on them!)
I know that popping happens because of water vapor expansion inside the kernel, so I had been concerned that unpopped kernels would have heat-induced damage that would lead to slow leaking of water over the course of the several months of storage, but apparently I needn't have been concerned; almost all of them were minimally viable. The mushroom shape, small size, and odd behavior in the popper indicates that they were less vigorous in popping, but I don't know whether they were always going to have trouble popping, or if the storage after heating had an effect. Not a difference I'm going to bother exploring, though.