Some items increase the saving throw DC of spells cast using them or while holding them. For example the Rod of the Pact Keeper says:

While holding this rod, you gain a +[1-3] bonus to spell attack rolls and to the saving throw DCs of your Warlock spells.

If a Warlock cast a multi-round spell, such as Hunger of Hadar, while holding a Rod of the Pact Keeper then stowed the rod to wield a weapon would the saving throw DC for the affected creatures drop?