When her MP's not recovering, you rezone? That means you're resummoning her, too. You can resummon an NPC without zoning. Just click on her to bring up the mini-menu and pick "Release," then cast her Trust spell again and she'll be back with full MP (provided it's been at least 3 minutes since the last time you summoned her).

Other than that, Trust NPCs have high hHMP and hMP between fights, so just try to take a 20 second break every now and then.