Shader global texture reset on scene load?

I'm generating a Texture3D with Perlin noise for use in a shader. It takes around 5-20 seconds depending on the resolution, so I'm doing so in a separate thread. Originally, I was generating the texture once the scene that uses it has loaded, but often the texture wouldn't be ready by the time I wanted it.

I changed the setup so that the texture is generated once when the game launches, and set like so:

Shader.SetGlobalTexture(PROP_NOISE_TEX, m_noiseTex);

However, after this change, the texture would sometimes be missing. I determined that the texture would only be correctly set if it completed generating after loading the scene that wants to use it. Any time I load a different scene, the texture seems to disappear and I need to run the above line of code again.

I can't find anything about this in the documentation, is this expected behaviour? Is it because an instance of the shader must be in use for the global properties to stay alive?