Probably the attempted coup by the "State Committee on the State of Emergency" or "Gang of Eight" in 1991. It basically created a crisis of legitimacy for the whole CPSU and Gorbachev in particular that it never really recovered from. Yeltsin on the other hand got boosted to the status of a national leader, for his prominent stand against the coup leaders. Prior to the coup there were a number of republics willing to sign on to the New Union Treaty, after the coup the USSR pretty much fragmented.

Stephn Kotkin's Armadgeddon Averted covers this fairly well, though I think he puts too much weight on the idea that the party essentially dissolved itself due to losing its supposed ideological reason to exist (ie. as leaders/representatives of the people).