Pokestops won't work if:
You're moving too fast
You're out of range
You've already spun it, but the game glitched and didn't show it as having been spun (now this updates next time it polls for pokemon though)
You're softbanned for spoofing or extreme GPS glitches (I got it once because as I got onto the subway in Boston, it briefly decided I was located somewhere along the pacific coast).
They're located in a park/location that has requested Niantic disable them while the park is closed, and the park is closed (in this case, they don't change shape to the blue circle when you approach, they stay as the small cube)
GamePress
Pokestop isn't working?
Anyone eles?
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Answers
It happened to me on a subway once. The game thought I was still at an earlier station and I made the mistake of spinning a stop. Then, a few seconds later, it updated to my actual location where I immediately tried to spin another stop, and BAM! got hit with a temporary soft ban. Lesson learned: don't spin two stops that are far away within a few seconds. Wait a minute instead.