Honestly, it is like saying "if I kill your chapter master, you lose chapter tactics". Arch demagogue devotions function more like chapter tactics than anything else. They modify the entire army, and rarely need the demagogue to stay alive for said changes to stay in place.
Dysorange nailed it, have him point out anywhere in the book where it says your AD needs to be alive/on the table for the effect to be in play. Or that it will end on death.
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