Stroke survivor's increasing fear of walking

[Charles-Cohen]

  My father experienced a significant stroke 12 years ago at age 63; through rehabilitation over the initial years, he learned to walk with a cane despite right-side paralysis.
  The quality of his gait began to wane a few years ago, but he continued to walk without much hesitation.
  In recent months, though, he has developed a more fearful attitude about walking.  On occasion, even in familiar places, he has "frozen", unwilling/unable to take another step unless he could lean on a wall or an adjacent person.  Uncharacteristically, he seems to resign himself to this situation rather than return to a rehabilitation facility to explore overcoming this problem.  He experienced two mild falls when attempting to lean over from a sitting position, but this situation preceded the falls.  
  Does this condition have a name/label for Internet research purposes?
  As described above, might the condition exceed the realm of physical rehabilitation and involve a psychologist, neurologist or other specialist?
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The symptom you describe, I feel exceeds the internet / search type
approach and you may well need an evaluation by a neurologist to see if
there is any thing else going on. Freezing can be due to fear or if due
to neurological mechanisms may be a symptom of Parkinson's disease when
it is termed BRADYKINESIA. This is usually a feature of late Parkinson's
but postural,instability and falls are also part of the picture.
I would suggest that you see a neurologist,ideally one with a special
interest in movement disorders to clarify this question.
If you wish to see a neurologist at the cleveland clinic the number for appointments
is [phone]