Summoning items with custom attributes doesn't include default attribtes

If you summon item (like an armor piece or a sword) with an attribute added to it, it will lose its natural attributes (like the generic.armor attribute, wich gives the player armor points), in order to get these natural attributes back, you need to add them to the command.
Here´s an example:

/summon Item ~ ~1 ~ {Item:{Count:1,id:leather_chestplate,tag:{display:{color:500,Name:Cool Blue Awesome Shirt},AttributeModifiers:[{Slot:torso,AttributeName:generic.maxHealth,Name:generic.maxHealth,Amount:20,Operation:0,UUIDLeast:1,UUIDMost:1}]}}}

This Leather Chestplate will lose its armor points, you will have to re-add them in the command.