Here is the Scenario:

These are customized banners that have been renamed. And I have a lot of different ones.

I am using barrels in this situation. I go to drop some off in a barrel only to have them drop to the ground when I exit the barrel screen. I have not tested this with chest, but it seems to happen more when I have a lot of different ones in my inventory or the barrel has a lot. I have logged out and back in several times and the issue persists. Sometimes they don't like to stack and sometimes they stick in my inventory too. It's hard to show in an image but I attached my F3 and a screenshot to give you an idea of how many banners I have.