Does the "Deputy of Arkham" card count as an item, for the purposes of counting up your total items when forced to lose half your items?
No, it does not count as an item
The Rules, page 16 note on the middle of the right hand column:
Important: When adding up items before discarding them, count all Common Items, Unique Items, and Spells. In addition, the Deputy’s Revolver and the Patrol Wagon both count as items. Allies, Skills, and other cards do not count towards this total.
Since "Deputy of Arkham" falls under "other cards", it does not count when adding up items.