How does vitamin A deficiency arise?
The WHO report "Global
 prevalence of
vitamin A deficiency
in populations
 at risk
1995–2005" (page 12 of 68) puts it like this: 


  Where animal source or fortified foods are minimally consumed, dietary
  adequacy must rely heavily on foods providing beta-carotene. However,
  while nutritious in many ways, a diet with modest amounts of
  vegetables and fruits as the sole source of vitamin A may not deliver
  adequate amounts, based on an intestinal carotenoid-to-retinol
  conversion ratio of 12:1 (2)  This ratio reflects a conversion
  efficiency that is about half that previously thought, leading to
  greater appreciation for why VAD may coexist in cultures that heavily
  depend on vegetables and fruits as their sole or main dietary source
  of vitamin A. 
  
  Usually, VAD develops in an environment of ecological, social and
  economical deprivation, in which a chronically deficient dietary
  intake of vitamin A coexists with severe infections, such as measles,
  and frequent infections causing diarrhoea and respiratory diseases
  that can lower intake through depressed appetite and absorption, and
  deplete body stores of vitamin A through excessive metabolism and
  excretion (3, 4). The consequent “synergism” can result in the body’s
  liver stores becoming depleted and peripheral tissue and serum retinol
  concentrations decreasing to deficient levels, raising the risks of
  xerophthalmia, further infection, other VADD and mortality.


Just as a side note: green leaves contain heaps of beta-carotenes as well!