I want to reclass Lucina to an archer. Doing so would remove her class C sword proficiency and replace it with class E in bows. But if I were to upgrade her to a bow knight later on, giving her the ability to use swords again, would she regain her C proficiency, or would she have to start over with E?
Yes, weapon proficiency is permanent to the character / unit, even if their current class doesn't allow them to use that weapon. When the character moves back into a class which allows use of that weapon, their previous proficiency level will be used.