The Johannesburg-based advisory company said the decline is likely to continue as South Africa is grappling with the consequences of nine years of worsening corruption and policy paralysis under former President Jacob Zuma.
The fragility of the economy may also limit the tenure of his successor, Cyril Ramaphosa, who faces his first national election May 8, Eunomix said.
"There is the strongest likelihood of him being a one-term president," the head of Eunomix, Claude Baissac, was quoted as saying by Bloomberg. "He is starting with a very weak economy, the weakest of any president since Mandela. He is also starting with a fairly weak hand from a political standpoint."
Only conflict-torn countries such as Mali, Ukraine, and Venezuela have had a worse time in the past decade than South Africa, said Eunomix.
According to the think tank, the major reason of the nation's massive decline is the unsustainable structure of South Africa's economy where economic power is largely held by an elite that wields little political influence.
"Economic policy serves narrow interests, thus generating insufficient and unfairly allocated growth. Populism, rather than developmentalism, is an easy temptation, with the economy a tug-of-war between mutually distrustful groups."
Eunomix also said that while Ramaphosa spent his first 14 months in power pledging a crackdown on corruption, an end to policy uncertainty and a drive to reform loss-making state-owned companies, his political weakness will hinder progress.
"South Africa's state performance peaked in 2007, that year its economy and governance were at their best. Since then the state has experienced continuous decline in all core indicators of performance."
"The developmental state project has failed. South Africa is now a fragile state, expected to continue to weaken," Eunomix said.