I don't think it ever goes away completely. I lost one of my cats last year, and I still cry sometimes when I think about him. I miss him terribly.
As for people, same thing. Do you still have some issues around that relationship? Something with which you need closure? Because that can cause lasting grief. My dad passed away 4 years ago, and I don't believe I have ever dealt with it. Maybe it's because he was losing his memory, and he wasn't the man I knew growing up, so maybe I had already let go of him before he passed away, but honestly, I don't know. One day I might wake up and my heart might be broken because he's gone. I may have pushed it down so deep, I just haven't seen it yet. I don't think so though. I think I accepted it before it happened.
I'm dealing with an ex-relationship now. We broke up about 6 months ago, but we still see each other almost every week, and talk on the phone a lot. But, we have serious communication issues. It is bewildering and infuriating and heartbreaking all at once. Honestly, right now the only way I am surviving and dealing with it is by having the Scarlette O'Hara attitude, of putting it off until tomorrow. Not something I would recommend.