I created a bunch of chests containing a lot of different banners, when I opened them, after about 6 to 7 chests the banners start to not be rendered anymore. I included a world download for ease of use with a bunch of chests with random banners. (Coordinates in case you get spawned in elsewhere are: -78 75 239)
Multiple people have confirmed this issue with me, so it's definitely a minecraft bug. I also had a completely vanilla client, so it's not the cause of a mod.