Well... I think, that one of the reasons is... well... he never knew her. I may have a biased point of view, but as a person, whose mother died during their childhood: You get used to it. Sure, if you knew the person, then there is a bit of trauma and sadness, but all in all you'll get used to it.
And Harry never knew his mother. I mean... why would you obsess about someone you never knew? Apart from becoming rather obsessed because of some kind of trauma, e.g.: bullying. You can't miss something you never had.
I also believe, that Harry is better this way. If you want to read about a PI who is obsessed about his missing mother, I recommend reading the Nightside series :) It's also quite funny.