The mayor hanged himself because he was wrongly accusedGracie's disappearance marked a turning point in Abe's career (namely, a bad one). Abe did what he could to solve it, but his investigation ended up in an accusation of murder - namely, one committed by Gracie's father. He hanged himself before he could face any jail time - only after that was it made clear that he had no involvement in Gracie's disappearance. That was the thing that brought Abe down in the eyes of the rest of the town.
- If Abe had been responsible for the mayor's death, you'd think that would be one of his primary regrets in life. He only seems to fee guilty about failing to save Gracie and has no problem keeping a picture of the mayor in his office. The mayor's suicide seems instead to simply be part of the town's degradation after Gracie's death and Abe's fall from grace.