I’m not sure if the intent of the game is to need to keep “Full Surge” in the loadout to maintain the effect. If that is not the intent, can the character sheet allow for the effect to stay when the card is moved to the vault?
Unless stated otherwise in the card, all Domain card effects can only be activated and remain active while they are in your Loadout. If you activate a Domain card with a long effect, and swap the card into your Vault before the effect would end, the effect ends early.