Retrieve notifications and share across browser tabs
I would try to also add a complete callback function to set running to false. It handles ( ("success", "notmodified", "nocontent", "error", "timeout", "abort", or "parsererror")) Those should be handled by error and success but something is going on, so give it a shot?

Other than, your code is quite solid, I ran JSHint over it, and it got very few hits. 


You never actually use notbox
You probably want to declare oldids before that if loop


Other than that 


The naming is definitely a mixed bag, I would stick everywhere with lowerCamelCase ( lastping -> lastPing, notif_body -> notificationsBody ( or consider notificationsElementor perhaps just notifications )
You are using one liner ifs without curly braces.


Final thought, are you at any point rebuilding the DOM? If you rebuild the DOM (specifically any of the elements captured by notif_ico and notif_body), then your code stops working.