As I'm sure the ICC would agree the communist movement has been extremely weak since the 1920's. In the 20th century many well intentioned workers joined the official so-called 'Communist' (in reality, Stalinist) Parties because the Stalinists could claim the historical prestige of having led so-called 'revolutions' and created so-called 'socialist' countries. Many other workers joined Trotskyist parties because the Trotskyists could claim the historical prestige be the true continuation of the Communist movement. Any other revolutionary movements found it harder to attract militants since they don't have the same resources or so-called historical 'successes'. How can real Communist organisations prevent potential militants from falling into these State Capitalist traps? Even those who see clearly that the Stalinists and Trotskyists support a system of 'state capitalism' masquarading as socialism might well erroneously conclude that socialism is impossible that the disasters of the 20th century are due to Marxism's theoretical positions on the State.
Fascism and Stalinism also weakened the communist movement through killing thousands of communist militants. The literal eradication of militants coupled with the atmosphere of terror and the traps of the Stalinists and Trotskyists meant that there was very little 'reproduction' of new militants. Yes the Left Communists are the theoretical descedents of Third international whilst it was still revolutionary but given the difficulties faced in the 20th century of creating actual constant organisations in addition to the minuscule size of current organisations it seems strange to claim any true continuation of the communist movement. Perhaps some kind of 'historical break' is needed, though what this would mean in theory or practice, I don't know.