The Smithsonian Institution continues to bleed to save itself as Sheila P. Burke, the Deputy Secretary and Chief Operating Officer, resigned yesterday. Burke was the second in command to Lawrence P. Small, who resigned as Secretary back in March. The Washington Post reports today that the Board of Regents isn’t taking the call for restructuring lightly, and Burke took the hit after her $1.6 million in compensation from outside activities came to light. The Regents…