What is the evidence for this? Most human behavorial genetics researchers talk about a "reaction surface" set for each individual by that individual's genes, but I'm not aware of any researcher who claims to have a proof for an upper limit in how much "general intelligence" (that would be IQ) can change in the case of individuals or in the case of populations. In fact, the existing OBSERVED degree of IQ increases all around the world
http://en.wikipedia.org/wiki/Flynn_effect
has been described by N. J. Mackintosh in these terms: "the data are surprising, demolish some long-cherished beliefs, and raise a number of other interesting issues along the way." (Mackintosh 1998, p. 104). You write, "no matter how hard you try," but it's not clear anyone is trying very hard or very systematically to raise anyone's general intellilgence, but it is happening anyway.
I meet weekly with human behavioral genetics researchers
http://www.psych.umn.edu/courses/fall09/mcguem/psy8935/defau...
and have learned from them that the whole field of human behavorial genetics is becoming much more conservative and cautious in its claims about genetic limits on human potential than it was ten years ago. That's what is said explicitly by Tom Bouchard, one of the most cited researchers in the field.
REFERENCE
Mackintosh, N. J. (1998). IQ and Human Intelligence. Oxford: Oxford University Press.
P.S. Other good, recent reading on this subject is
Neisser, Ulric (Ed.) (1998). The Rising Curve: Long-Term Gains in IQ and Related Measures. Washington, DC: American Psychological Association.
Flynn, James R. (2009). What Is Intelligence: Beyond the Flynn Effect. Cambridge: Cambridge University Press.