Once technology progresses far enough, do you think that mizar could ever show back up as an artificial intelligence?

No.

AI and reincarnations are not the same. Al-V is an AI; he is not Alcor. If, and this is a hell of an if, if Alcor ever made an AI based on his memories of Mabel, he might be able to make something with a similar personality, but it would not be the same, and it would definitely not be her. He knows and understands this and therefore will not be doing such a thing.