I made a texture pack with a custom texture for an Illager banner (size = 512x512).

When I load my world with the texture pack active while connected to the internet there is no problem and the texture loads how it's supposed to.

But when I load the world without internet connection, the banner texture (and only the banner texture, everything else works fine) is just the default texture. 

I tested this out with and when I try this with a texture of the size 128x128 or lower, there is no problem. Maybe it's due to the size (512x512) that is a bit big?