Ion Shield integrity scales a shield’s defensive contribution and is reduced by every direct attack. Source
Evidence status — confirmed: Unless noted otherwise, mechanics are verified against the installed patch 11.73 guide.
Every Attack chips Ion Shield integrity even if the attackers die:
base damage % = attacker opening power / 45,000
ratio = attacker power / defender power
blend = ratio / (ratio + 1)
factor = 0.90 + 0.20 × blend
integrity damage = base damage × factor
Only siege removes actual building levels. Integrity attrition, however, can prepare a later breach.