Q:

What is the name of a condition where one cannot/can poorly perceive depth for objects moving towards them

I remember a case where someone apparently had great difficulty perceiving the distance of an object if it was (quickly) travelling towards them. Their depth perception was otherwise fine, but when, for instance, catching a ball, that person could not accurately gauge depth and seemed to rely on guesswork/other cues (size of the object? timing?) to decide when to attempt to catch it. Hand-eye coordination was not a problem, and for slow-moving objects (for instance, rolling a ball across the floor) there was no problem. What is the name of this condition, and what could be likely causes?

A:

What you appear to be describing is called Akinetopsia.
(Greek: a for "without", kine for "to move" and opsia for "seeing")

a neuropsychological disorder in which a patient cannot perceive
  motion in their visual field, despite being able to see stationary
  objects without issue [...]
   There are varying degrees of akinetopsia: from seeing motion as a cinema reel to an inability to discriminate any motion. There is currently no effective treatment or cure for akinetopsia. 

Causes range from brain lesions to dementia, certain medications such as antidepressants (nefazodone) and halucinogens such as LSD. It may be induced artificially by Transcranial magnetic stimulation.

