The tradition has generally been to re-appoint Fed chairmans originally appointed by presidents from the other party. Paul Volcker was re-appointed by Reagan, and after Reagan later appointed Greenspan, not only Bush Sr. and Jr. re-appointed him, but also Clinton. So it shouldn't be too shocking that Obama re-appointed Bernanke.
Right now the narrative is that Bernanke "saved America and the world from a depression". Something which ignores first of all how Bernanke as member of the Fed board supported the Greenspan policies which created the problems in the first place, and secondly also ignores how the Fed really hasn't solved the problems.
While it is likely that growth turned positive in the third quarter, the risk is very high of a double-dip recession or a dramatic increase in price inflation-or both.