If you keep both eyes open, you will not forget to close one in the heat of the moment....
Also, when shooting rifle or bow, with both eyes open, your brain receives more light input which allows your pupils to be dilated smaller. This gives you more depth of field and a greater range of the world that is in focus.
Both open also allows you to see stuff sneaking up on your "off" eye side more easily. Unless you shoot non-dominant, or your eyes are really close to equally dominant and tend to switch back and forth, you should not have a problem with both open.