No. A person can certainly change from being sexual to "having no sexual feelings or desires, or who is not sexually attracted to anyone." Hormonal changes can do this. Sexual trauma (abuse/rape) can do this. Mental illness can do this (e.g. severe depression). Medication can do this. Just to name a few. I don't get why that would seem impossible.
If you no longer have sexual feelings due to any of those reasons, you would not be considered asexual. I think we're talking about different things, which is why there's confusion. Maybe the word can be used both ways, I don't know. In my opinion, that's just confusing and your examples don't need to take the word, but if someone prefers the label, I don't see any problem with that.