While some people state Vampyres are immortal and will live forever, this is sadly not true. Lets look at this statement for a second or two. If a person found a way to live forever, do you not think everyone in the world or at least the extremely wealthy would have found a way to become a Vampyre by now.
The immortal Vampyre is simply or should simply be referring to ones soul. Many religious theorists believe humans have immortal souls, not just those following the Vampyre Path. Christianity has long held the belief of an immortal soul.
The bottom line is, a Vampyre in any form is human, though could have a different spirit residing in him or her. If the person is shot and does not receive medical attention, he or she will come to a physical death just as any other human. Will the persons soul continue? Sure