Low red blood cell production is called “ablastic anemia”. I don’t know why they said there’s no name for it.
Good question.
You’re thinking of aPlastic anemia http://en.wikipedia.org/wiki/Aplastic_anemia , but that involves the white blood cells as well. This sounds like some form of pure red cell aplasia http://en.wikipedia.org/wiki/Acquired_pure_red_cell_aplasia , but there may be details that didn’t match up with known forms of that (from the skimpy Wikipedia entry, it appears that red cell aplasia generally involves some autoimmune and/or infectious process, meaning red cells are getting destroyed, rather than not produced in the first place).
From another article:
“Doctors believe his condition is unique, but said it is similar to Diamond Blackfan Anaemia (DBA) - but some of his symptoms were very different.”
http://www.dailymail.co.uk/health/article-1139624/Boy-baffling-illness-rare-does-cured-PARENTS.html
Maybe his symptoms are similar but different to the point of being a different disease.