While concussions on their own won't kill him, Jace still has to worry about bleeding on the brain or between the lining of the brain and the skull. With this kind of injury a person can seem fine at first but, depending on the type of bleed, can deteriorate in a matter of hours or days and eventually lead to death. Dizziness and disorientation are common symptoms of these types of injuries. This is how Natasha Richardson died.
It is especially dangerous to Jace as he's already regularly experiencing such symptoms as vomiting and disorientation. He may not catch the warning sign.

