Hello my name is Sarah too!
We had the same problem with my dog, Duke. Okay he didn't kill a baby goat but he always ran out of the invisible fence. He would take the shock and go on. It depends how old the dog is. Duke used to run out of the invisible fence when he was 2 or 3 years old. As he got older the shock didn't bother him anymore. Now he is 9 years old and we have a very strong invisible fence. I think the type you have is the type that only shocks him once. The one we have is different. It keeps on shocking him until he comes back into the safe zone. If you don't want to send him to rescue try considering a stronger fence. I hope this helps!

Sarah