The Banner of Storm's eye (Magic Item Compendium pg 151) States:
As long as it is held aloft, the banner automatically suppresses (but does not dispel) fear effects on all creatures within 20 feet. It also prevents any creature within 20 feet from becoming confused or stunned.
A mummy's despair ability reads:
Despair (Su) At the mere sight of a mummy, the viewer must succeed on a DC 16 Will save or be paralyzed with fear for 1d4 rounds. Whether or not the save is successful, that creature cannot be affected again by the same mummy’s despair ability for 24 hours. The save DC is Charisma-based.
I get that the banner "Suppress" the effects of paralysis while within 20 ft of the banner as despair is a fear effect. But how exactly does this function in game?
Would the players roll for the save upon seeing the mummy and while within the radius of the banner, and then if they left the radius they would become paralyzed if they failed the save? I guess the "suppresses" word has me scratching my head a bit.