Current abortion law is largely based on medical definitions. In particular, what defines a human being as a living person. Specifically, brain activity. Prior to about 21 weeks, there is no measurable brain activity in a fetus that is sustained in such a way as to meet the definition for being alive. If they were separated from the mother, they would be considered dead, taken to the morgue, and processed. We have firm, clear lines drawn for precisely when a human ceases to be a legal person; when they have died. This extends even to brain-death, where the body may still be on life support, but the individual is ruled to be deceased due to the complete lack of brain activity.
Since we have clearly defined rules for when a person can cease to be a living human being, with all the rights thereof, it stands to reason we also need rules for when they become a living human being. And those are what create restrictions on abortions.
So no. People are demonstrably not "always a person forevermore".
Plus, you included your own error in your own phrase, with the word "once". You yourself admit that there is a point where a human being comes into being. You haven't given any rational justification for why that point is conception. It's already defined under the law, and again, that's what restricts abortions already. A 12 week old fetus has not become a human person. It isn't at that "once a human" stage. There is no inconsistency under the law, but there's a ream of it in your arguments.