It's very consistent for me so I don't think its model related. I just tried with a simple cube and I get the same problem.
I don't get any errors in the console when I attempt to import the textures but I think I might have found something to help narrow down the problem though:
My texture is a 64x64 png. When I try to upload the png it doesn't import like before (using both the "Import" button from the "Materials" tab and the "Import" button from the "Textures" window) but when I upload something a bit larger like a 512x512 png, that file uploads with no problem then my 64x64 textures are able to upload from that point on.
When I first open the draft I do get this list of errors in the console. This is before editing the scene at all and just opening it right after upload:
Once I get the textures to import using that method I stated before, I get the following errors when aplying them to the cube. The first error is when I apply the 64x64 png (Blue texture) and the second error is when I apply the 512x512 png (Sandy Texture).
Thanks and I hope this helps