Does grenadine need to be refrigerated? I've been looking for a bottle of Rose's Grenadine for quite a while without luck, so when I saw a big ol' liter of Llord's at the liquor store, I grabbed it. I'm not sure I want to allocate that much fridge space to it though. Can I keep it behind the bar instead?

Sugar is a preservative and there's a little bit of alcohol in it too, so my guess is it's ok on the shelf.
I'm not sure about other types of grenadine, but assuming they're the same as Rose's, they do not need to be refrigerated.

It's not just that they contain sugar - they're practically nothing but sugar, water, and a couple of "chemicals."  There's really nothing in there that can spoil, unless you put something else into the bottle that wasn't there originally.

Unless you accidentally dropped a piece of chicken in there, definitely don't worry about refrigeration.  It can sit on the shelf.