Just had a run in with a Word Bearer Decimator (those big robotic guys that get a shield from three nearby pylons).
I destroyed the three pylons, but the Decimator kept its shield!
I used my guns to wear down the Decimator's shield/armor bar down to 0%, but still the Decimator kept its shield.
I walked away, killed other enemies and came back: The Decimator still had the shield!
Thus the Decimator can not be destroyed at all, because the shield does not go away.