Only Once
this only happened to me once.
In a random Battle, Against a Foe's Mightyena that had used Howl once, (1.5x att) My Arbok's intimidate activated, and its attack did not drop. It clearly had Moxie as it's ability, and I was switching from an Umbreon, so no Pokemon had been defeated.
It wasn't a huge deal, as he used howl again (which did bring it up to 2x, which is when I tried to understand what was happening... much to my avail) and I cannot think of any items that would prevent status lowering without showing activation of the item. Besides, I'm almost positive he had Leftovers.
It's just something I thought I should post
It isn't a big deal, and I ended up losing because He had a Kyurem-Black with outrage, not because of the Mightyena.