Multiple 1024x1024 texture pages or one 2048x2048 texture page?

I have a lot of textures around the size of 512x512, and the LibGDX texture packer can't find a way to put more than one of those on one page for some reason. So, I end up with fifteen or sixteen pages, the majority of them being mostly empty - even really small textures don't get put on them. If I change the max size to 2048x2048, however, I can fit everything on four pages. This cuts loading times on certain stages in half, but apparently some devices don't support textures about 1024x1024. Do texture pages also have that restriction? Should I go back to smaller page sizes?

Thanks.