Well the first thing is that they really didn't lose that much in fact of all the major parties from before the rise of the Nazis the SPD remained the strongest. However it is true that they did lose some amount of support in the mid 30s. As for why it is a fairly simple answer. People were sick and tired of the Weimar Republic, constant coalitions which mostly did not accomplish anything or last long weighed heavily on people's minds. As a result old parties began to fall in support. Now where did this support go? In the case of the SPD it mostly went to the Communist Party. Now the interesting thing to note with this is that by the mid 1930s the majority or near majority were voting for the Nazis or the Communists both parties that ran on a anti Republic platform.

So in conclusion the SPD remained a strong party right up until the end of the Weimar Republic been either the first or second largest party and what support it did lose went to the Communist Party that considered the SPD to be the biggest enemy.

Source The Coming of the Third Reich Richard Evans.