You'll spoil this wonderful, subtle movie. Therefore I plead to all of you who want to the see this movie. Do not watch the trailer. I was lucky to watch this movie unbiased and untainted without even seeing the trailer.
Keaton was suicidal. He tried to kill himself at the end of the movie. My interpretation was, he was so taken aback by the fact that Kelly/Kate had seen Keaton in a totally new light. He couldn't go back to her because she knew that he was a contract killer. I.e. the scene with the two of them in the church. Had she not found out about his other vocation then they would have lived happily ever after. Hope that clears up things.
ps the best line in the movie was perhaps where the two cops are at the motel investigating Kate's abusive ex,"She's your girlfriend." Priceless!
He WAS suicidal. the girl saved him from that permanently. His last "suicide attempt" was fake so the cops would close the case and leave the girl alone.
They set it up early on that the cops loved when the criminals killed themselves. He fixed so that they'd believe the killer was now at the bottom of the lake or river.
That WAS the plan, until he realized that someone had pulled over and saw him hanging out on the bridge. So he went and fetched his hat and probably resorted to a different escape plan...