I feel like you should not lose your sigils when you are fighting in the battle standard Flags.
Sigils are lost upon death unless you have the Sigil of the Fiend applied. Concerning the Battle Standard flags, if you’re using them to teleport between places, you need to consider your sigil loadout when removing your bracelet if you’re just trying to warp from one base to another. If you’re actually doing a player vs player fight under the battle standard in someone’s arena, then if you have sigils and you die, that’s just how it is. Sigil of the Fiend is your friend to keep others upon death. If you’re battling other players, don’t use sigils. If you’re teleporting between bases, either apply them after or use Fiend.