Are you sure that the Wing anti-ice switch is OFF?
The wing anti-ice should only operate in the air.
what would cause the APU Bleed valve to modulate closed?
Probably best not to use the term "modulate".... It only has two basic positions. Open or closed. Well, not including "in transit". No spring-loading, no servo air. If it loses
AC power, it freezes in the last position. If it loses DC control power (only), it closes. Ref SSM 36-11-03
I can't see it being commanded closed to stop the APU shutting down. With a tired APU, all I've seen are duct pressures going down and down until you start getting yellow numbers on the ECS synoptic.
Changed the Bleed Valve yesterday no effect.
I can't see how it would cause a problem like this. It's just a DC motor attached to a butterfly. It needs an external command to move.