The Wikipedia article about the organization only addresses this question with the lines "This is more than the SPD leaders wanted, but SPD workers grew increasingly revolutionary. In 1933, the organization was banned.".
Could one of our illustrious experts on Weimar Germany shed some light on this subject?
It wasn't really a matter of the SPD 'wanting' to ban the Iron Front, as both the Iron Front and the SPD, along with many other German opposition parties, were banned in 1933 in the aftermath of the Reichstag Fire and the passage of the Enabling Act. The Iron Front was not solely an SPD institution either-it incorporated the elements of several other paramilitary forces, such as the 'moderate' paramilitary of the Reichsbanner Schartz-Rot-Gold, into a "united" front against the paramilitaries of the ultra-conservatives and the Nazis (such as the Stahlhelm and the SA). They were also technically opposed to the Rotfront, the KPD's paramilitary arm as well.