Aha! I think I know what it is!
FS2 short-circuits evaluation of sexps once they become true. For example, with the "is-destroyed-delay" sexp, FS2 replaces that sexp internally with "true" once the ship is destroyed. Since the ship isn't coming back from the dead (we hope), the sexp no longer wastes time on evaluation.
Key-pressed seems to be one of those sexps that is short-circuited. As soon as the key is pressed, the sexp is overwritten with "true". This means that as soon as the sexp repeats, it thinks the key is still being pressed and so it re-executes as soon as the repeat delay is up.
That's why every-time works... because it resets the entire sexp tree to "unknown" after it's evaluated. Aside from flushing the tree it's exactly the same as when.
The solution is to add key-pressed to the list of sexps that aren't short-circuited, but that might screw up something else. And that doesn't explain (1-4) acting differently from other keys.