I know what you mean about Carbuncle - I love the summon and when I learnt White Mage used Arcanist as a sub class I kinda hoped it allowed White Mages to use Carbuncles as well (I know it wouldn't do much, but I can hope).

Anyhows from what I found out so far levelling up my Summoner you do not lose Carbuncle at all and can keep summoning it as normal. Only Scholars lose Carbuncle until change back to Arcanist or switch to Summoner.

Ignore that, having looked it up it seems you lose them for Titan etc