"If you hold a lungful of air, you can survive in the total vacuum of space for about thirty seconds."
nope nope you would first die, then after 2 minutes which is when you would be dead you would regen and come back just to continue your loop, (I think its 2 minutes before the brain shuts down anyway... might be 30 sec but I am almost sure its 2 minutes a human can "survive" in vacum.
With all of that in mind, an instantly regenerating body would have no real need for oxygen (or anything for that matter) and so hypothetically it would not die in space at all. Any damaged or dying cells would be instantly replaced with new ones. Now if the regeneration were slower these would be very real concerns, but not when we're talking about 'instant' regeneration.