This book seems to suggest the Soulless one can regenerate indefinitely when they die:
http://www.uesp.net/wiki/Lore:Chaotic_Creatia:_The_Azure_Plasm
So is the Soulless one a mortal?
Source:
"Then there are the poor slaves known as the Soul Shriven. Each is a mortal kidnapped from Mundus at the moment of death, his or her soul stolen by Molag Bal for some unthinkable purpose, and given in exchange the vestige that enables him or her to form a counterfeit body here in Coldharbour. But they are not native to Oblivion, so a Soul Shriven's body is a sad imitation of the body worn in life, suffering rapid wear and decay until it dies—a death that is no liberation, for its vestige only forms a body once again, over and over, ad infinitum...
Such are the facts. What follows is speculation, born of conversations with the Sojourner during his infrequent and unpredictable visits. His theory is that the Soul Shriven's bodies are flawed because they have lost the focusing principle of their Anuic souls, so their vestiges are imperfect patterns. I concurred that this was likely, and then proposed the theoretical possibility of a Soul Shriven who, despite having lost his or her soul, possessed some other intrinsic Anuic aspect. This shall-we-say "paragon" Soul Shriven would form an unflawed body in Coldharbour that was a perfect duplicate of the body worn in Mundus. In fact, if this paragon bore a sufficiently high Anuic valence, upon contact with Padomaic creatia its body would form almost instantaneously.
The Sojourner scoffed at my theory, but seemed taken with the idea nonetheless. He went on to speculate that if such a thing were possible, it would probably occur in a situation where the Mundus was in existential jeopardy. In that case the Heart of Nirn would spontaneously generate such "paragon" individuals as a way of defending itself from destruction, in a manner analogous to the way the mortal body fights off infection."