I would say that mostly depends on how well you were able to heal from the first one. The worst-case scenario is when you get injured prior to full recovery from the first injury. That's when you see the very dramatic and sad cases of kids who die from recurrence of a head injury after returning to play before being asymptomatic. That's what we don't want.
There is more and more information on the spectrum of what I just described. Without dying, you get those very bad and long-lasting episodes of concussions when you get reinjured prior to healing properly.
On the other side, there's no real indication that if you sustain one concussion, heal from it very well, and make a successful return to the sport you love that you will have residual weakness.