Yes, hypervigilance can fatigue. When you are hypervigilant, you are in a hyperarousal state in which you are on guard and alert to the possibility that danger may be lurking. This hyperarousal state is often associated with PTSD (post traumatic stress disorder).
So when you have endured a life-threatening trauma and you develop PTSD, then you will have hypervigilance, and this hyperarousal state takes much energy to sustain over long periods of time. This hyperarousal state was only meant to be effective for survival over the short-term, to deal with an immediate threat.
However, when you have PTSD, then your hyperarousal state continues beyond what it was designed to do, which is to be on guard to any danger that may harm you imminently. So the hypervigilance with PTSD can last a long time, and soon, your body rebels and you develop fatigue.