* Major U.S. stock indexes fall in possible reversal of rally * Euro down after early gains on ECB cash injection * Oil prices extend losses for a third day By Barani Krishnan and Herbert Lash NEW YORK Feb 29 (Reuters) - U.S. stocks reversed early gains in late morning trade on Wednesday , prompting questions on whether the market's slow and steady rally of the past few months was about to end, amid an unexpected selloff in the euro. The market's reversal came after bearish remarks on the U.S. economy, in particular the country's job market, by Federal Reserve Chairman Ben Bernanke, which some traders said may have accelerated the declines. Two hours after the open, the Dow Jones industrial average was down 57.52 points, or 0.44 percent, at 12,947.60. The Standard & Poor's 500 Index was down 5.94 points, or 0.43 percent, at 1,366.24. The Nasdaq Composite Index was down 13.08 points, or 0.44 percent, at 2,973.68. The euro hit a session low of $1.3346 against the greenback. Oil prices fell for a third straight day, with London's Brent crude down 0.6 percent at $120.84 a barrel.