So essentially, my avatar's skin just disappears at random. Based on what I remember, my avatar's skin was the Enderman In A Suit skin from the first Battle and Beasts skin pack.

The next world I played had my avatar turn into Steve. The next one after that made my avatar completely invisible! Even if he was wearing armor, he would be completely invisible!

Based on what I did to my Xbox One, the problem seems to be caused by not having an internet connection. This would cause the Marketplace to fail to load, hence my skins would also fail to load, as they are managed by the Marketplace. I also cannot make a new skin, as the "Create Character" button is unselectable until all the skins have loaded - in this case, it will never become selectable.