I'm not exactly sure what you mean, but if I understand correctly, you're asking at what point does mourning become whiny, in the context of a narrative?
I think probably the answer is: when you start repeating yourself. Mourning can be difficult to write for this reason, but I think you have to attribute some intelligence to your readers, so that they can assume, even though you've stopped explicitly talking about how much the protagonist feels sad, that his feelings haven't just gone away and moved on to the next thing. Obviously you can continue referring to it occasionally, but commenting that he does every action "miserably" or "with an air of melancholy" is probably gonna make him seem like a manic depressive on a come down.
As to how much "real world" time this takes? I think that depends on his relationship with the deceased. Remember you can always skip over this time with your magic narrator powers...