It's a person.
A loved one.
Someone who has a name, a relationship, a special place in a grieving person's heart. To call that a "loss" is so impersonal.
Perhaps I'm alone in feeling this way, perhaps other bereaved people don't mind hearing "I'm sorry for your loss", but to me, when Verd passed away, it was almost insulting. He was, IS, so much more than "my loss".
My brother's girlfriend's father just passed away in his sleep. My childhood best friend just lost her mother to cancer, and all over Facebook I keep seeing, "I'm sorry for your loss". Ugh.
I realize people don't know what to say, that speaking about death or talking to someone who is walking the agonizing path of grief is difficult for some people, but please take this to heart: It is comforting to hear the name of the loved one you are so desperately missing.
If it isn't comfortable for you to say the name of the deceased, then say their relationship to the person you are trying to console. A simple, "I'm so very sorry to hear about your mother/uncle/sister/friend." or, "Your dad sure seemed like a wonderful man." and offer a hug.
Or better yet, offer a memory you have of the person who passed away, because memories are the only thing those of us left behind have. Memories. A way to hold someone close to your heart, when you can't hold them close to your body anymore.
Not a loss. So, so, so much, not a "loss".