Humans are essentially unsatisfied creatures - if you take a starving dog out of the rain and feed him, he will love you forever.   After a few weeks of nice treatment, many humans will decide they deserved to be taken out of the rain and maybe even that they are doing you a favor.

So it goes with wealth.   Money does buy happiness, contrary to folk wisdom - it just doesn't last.  In the case of entire nations that get a better standard of living, after about a decade happiness is no longer rising with wealth.   Let's not kid ourselves, people in wealthier nations are happier, on average, than people in poor ones, but it does not rise forever.

So if wealth and happiness are positively correlated, why doesn't happiness continue to rise?  That's the paradox.

A new study in PNAS sought to examine this paradox in more detail, easier now because there is readily available data from former poor Eastern bloc countries rather than just developed ones.    The happiness-income hasn't gone unchallenged since its original formulation but the researchers state those were short-term blips and that their new data, based on nearly 40 countries over at least a decade, bear that out.
Aside from the logic of 'money does not buy happiness' how happiness is measured would seem to be too inconsistent across cultures.    The researchers believe by taking such a large number of countries they factor that out - but happiness has a different inflection point for individuals so it's hard to determine how successful they are.

Some humans do remain completely happy in a safe, content environment and don't suffer a drop in contentment with time so matching GDP to personal satisfaction may not be in the realm of science just yet.

Citation: Richard A. Easterlin, Laura Angelescu McVey, Malgorzata Switek, Onnicha Sawangfa, and Jacqueline Smith Zweig, 'The happiness–income paradox revisited', PNAS doi: 10.1073/pnas.1015962107