ABANDONED. cyberpunk robot cop gets killed over and over

[Spottyblanket]

The book is in a cyberpunk setting, it has a dark blue cover.
I remeber there being a number in the title.
The main character is a robot, android cop and has to solve a murder however he keeps getting destroyed each time and an updated version comes out. He becomes more and more human with each passing update. I remember it being darkly comical as his earlier forms have no idea how to interact with humans.
I also remember there being characters who loved jazz.

[Lobstergirl, au gratin]

When did you read it or about when was it published? Series or standalone? Author female or male?

[Spottyblanket]

I believe author was male. Standalone as far as I remember. I wqnt to say 2006 ish.

[Lobstergirl, au gratin]

Spottyblanket left the group. Moving to Abandoned.