This is the first time I've heard any reference to "long" vs "short" vowels since I joined EF three years ago!
I'm not having much luck waking up my brain, but I'd say that as an article, it's never pronounced as a long "a," as in "hate," nor is it pronounced as a short "a," as in "hat." It's pronounced as an "uh," as in "hug." He picked up uh ball.
You pronounce it long a if you are a rather slow-witted child just learning to read or if you are Jim Lehrer reading the news on PBS's News Hour. Otherwise, you pronounce it like the u in but.