This only happens if you have Sharing is Caring. You're getting two times the health penalty indicated on the Hoplite shield's stats. Your health is already decreased because your own shield, and when you summon DT, he has a copy of the Hoplite as well, but the -health penalty of his shield will be applied to you. So that's why your health is going to 0 when you summon DT. Hope that explains it.
It's raining luggage and babies and limbs and Daddy doesn't come home.