I had 1 Banner of a specific type (purple with blue gradient, cyan skull, top black say, bottom black saw) and I place quite a few on the top of one another, and on the sides, then I broke a bottom one, thus making the others on the top fall as item drops, which is normal. Then when I picked them up, they all went into my inventory and stacked, but not with the original one that was already in my inventory, and so I tried to stack them, and they wouldn't.
In the pictures, I show that they are the exact same kind, so they should stack, but they won't.