Shouting gets disabled the moment I need it most?
Solution 1:
I've done a bit of testing, and stagger definitely prevents shouting. Notably, I've been unable to shout until the camera stopped shaking after a dragon landed nearby. Being staggered by other enemies produces the same result, which isn't really surprising, considering attacking and spellcasting are also impossible while staggered.
Also, I've experienced shouts remaining disabled after a stagger for a few seconds, but it only happens occasionally, which seems to be a minor bug.