Refrigerating Clam Juice
It should keep in the fridge for a week or two- and you should be able to smell it if it goes bad.  However, you can just freeze any unused juice in 1 or 2 Tablespoon portions (in an ice cube tray) and keep it around for the next time you need it.  Just transfer the frozen cubes into a labelled freezer bag so they don't get lost or thrown out.  Waste not, want not, right?