Build America Bonds Extension Act of 2011 - Amends the Internal Revenue Code, with respect to the Build America Bond program, to: (1) extend until December 31, 2012, the authority to issue such bonds and the authority for payments to issuers of such bonds, (2) reduce the percentage rate of payments to issuers, (3) incorporate in the definition of "Build American bond" certain tax-exempt private activity bonds, and (4) allow refundings of currently issued Build America bonds.