Death caused by "Failure to Thrive" (FTT)
The reason for failure to thrive other than insufficient nutrition, can be suppressed growth hormone secretion due to emotional neglect. In the following example, both the emotional neglect and insufficient nutrition were combined, though:

Psychosocially stunted growth masked as growth hormone deficiency, (Klinische Pediatrie, 1999):


  Short stature is a common reason for presenting a child to the
  pediatrician. Emotional deprivation may cause short stature and may
  simulate growth hormone deficiency. Diagnosis of emotional
  deprivation as the cause of growth retardation is difficult and
  misdiagnosed frequently despite of suspicious clinical signs. We
  report on 2 patients with growth retardation because of emotional
  deprivation. At the age of 5 years both children had a severe growth
  hormone deficiency. They received therapy with growth hormone and
  showed an increase of growth velocity to > or = 8 cm in the first year
  of treatment. But in the third year of treatment both patients showed
  a diminished response to the growth hormone therapy. During the period
  of observation the features of emotional deprivation became obvious
  through the extreme behavioural abnormalities. Both children showed
  disturbances in their social behaviour, and striking disorders
  concerning eating and digestion. The families of these children had
  severe social problems; alcoholism, low income and rejection of the
  child were risk factors. Removal from the current environment led to
  a characteristic increase of the growth velocity. Growth hormone
  deficiency was spontaneously reversible, so that treatment with growth
  hormone was terminated. The social environment and the psychical
  prosperity are essential growth factors in childhood and adolescence.
  The common features and risk factors of emotional deprivation are
  described. Spontaneous catch-up growth after removal from the
  current environment distinguishes this form of short stature from the
  other organic growth disorders.


Hopkins Medicine says that:


  Other factors that may lead to failure to thrive:
  
  
  Emotional deprivation as a result of parental withdrawal, rejection or
  hostility
  


and 


  Problems with the endocrine system, such as thyroid hormone
  deficiency, growth hormone deficiency or other hormone deficiencies...


...some of which might be triggered by emotional neglect despite proper nutrition:

Failure to grow: lack of food or lack of love? (Professional Care of Mother and Child, 1994):


  One of the most important criteria for good health in childhood is
  normal growth. Taking regular accurate measurements of length and
  plotting them on a centile chart is essential to spot early signs of
  growth disorders. Be alert for a "zig-zag" pattern on the chart: it
  could indicate psychosocial dwarfism (see opposite). Length is
  more important than weight for identifying growth disorders. Lack of
  love, or an adverse emotional or social environment, can cause growth
  failure even in a child who is eating enough. Such children have a
  condition called psychosocial dwarfism, which is due to
  hypopituitarism (too little growth hormone secretion from the pituitary gland). This condition does not respond to growth hormone
  treatment. Once the child is placed in an alternative environment, eg
  a good foster home, the hypopituitarism is reversed and rapid
  "catch-up" growth takes place. It often emerges that such children
  have been physically, emotionally or sexually abused.


I'm not aware of any case in which psychological reasons alone in a properly fed child would result in death associated with failure to thrive. When it comes to failure to thrive in certain orphanges, I would not ascribe it solely to psychological reasons...