Do people who experience heautoscopy become unable to see their reflected image in a mirror?

While acknowledging the fact that Google delivers personalized results, I am fairly sure a Google search for "heautoscopy" will deliver you bucket loads of papers to read - I have copied a random handful for your convenience below under 'further reading'.

However, a popular source seems to contradict your definition, as it states heautoscopy as being:

A hallucination in which one sees one's own body from a distance. Heautoscopy may occur as a symptom in schizophrenia and epilepsy.

Your own referenced Brugger (2002) paper gives a nice definition of both terms in one go:

In an autoscopic hallucination the observer's perspective is clearly body-centred, and the visual image of one's own body appears as a mirror reversal. Heautoscopy (i.e., the encounter with an alter ego or doppelgänger), is defined as a reduplication not only of bodily appearance, but also of aspects of one's psychological self.

Not being able to see ones own reflection in a mirror would be an entirely different phenomenon, more akin to mirrored-self misidentification

<sub>Further reading
- Blanke & Mohr, Brain Res Brain Res Rev (2005); 50(1): 184-99
- Brugger, Cogn Neuropsychiatry (2002); 7(3): 179-94
- Brugger et al., J Neurol Neurosurg Psychiatry (1994); 57(7): 838–39</sub>