I looked into this and found that adding:
"ClosingRadius = 9," to
C:\Program Files\Stardock Games\Demigod\ddddgdata\units\heroes\HQueen\HQueenEnt_unit.bp seemed to have fixed the problem.
My best guess to the problem is that the closingRadius defaults to the maximum weapon range (14 for the Shamblers) or to a default value (20 seems about right, distances are rather small and I didn't see the point in testing it that much). However due to the mathemetics involved in calculating range, this is occasionally out of range. You'll notice that for all other ranged minions have a ClosingRadius value that is less than their maximum range.
This in range/out of range problem is only apparent when targeting nonmoving units, that is towers. Other units typically close the distance to the shamblers to engage them. This puts them in range and lets the shamblers shoot at them. However the towers will not close the distance, and so the Shambler moves to ClosingRadius distance, and since they are usually out of range (except in the case that they are jostled closer or move too far) be unable to shoot at them. However, they "think" they are in range and so keep locked onto the tower, never firing. You'll also notice that in this situation, when other targets come into range of the Shambler, the Shambler will not fire at these closer targets. The shambler is waiting for the tower to get closer and it has priority targetting. This may also explain why Shamblers are typically seen to do less damage than they should, they are forever outside of their weapon range even though they think they aren't.
Another QoT bug or glitch perhaps is the rendering of her Basic Attack (Roots coming up from the ground). The begining of the attack animation is fine, a root juts out of the ground striking the target and then retreats into the ground. However, if you watch on a map that has bridges or other structures that allow the ground underneath the combat area to be seen, you can see the root retreat down a ways before disappearing after the attack. The later half of this animation should be removed. This is, of course, only true if this is a generic issue, and not just a special feature of my graphics card.