I'm seeing this bug in version 0.86, too.
Just as you said, the archer fires slowly about half the time, and about a quarter of the time it acts as if it fired but never does damage to the enemy.
If it's the same as the bug with bows in WOM, the speed issue will get significantly worse if you have mounted units in your stack. In WOM, the archer's speed would slow down to around 10 to 20 seconds before it would fire when there were mounted units present.
I used to see this bug all the time in WOM, and I'm a bit disappointed that it's still here.