Is this still a problem?

Placing the wallpaper image file into my Pictures folder solved this for me.

Yes it is still a problem.

I can't reproduce this with latest Solus MATE. I was able to open images with Eye of Mate, set as desktop background, and the background is still present after reboot.
I tested with images in my pictures folder, and one in .local/share/, the wallpaper remains after reboot just fine.

@TheMooseIsLoose I think the problem here is that if you want to have a custom background, you have to manually save a copy of the image file in the Pictures folder. I would expect to download a background image file to my Desktop, open it in the Mate image viewer, set it as my background, then delete the original image from my Desktop and still have that background after restart. Setting as background should automatically save a copy of the image to /usr/share/backgrounds/solus.
Right now I moved my background image file from Pictures to Downloads, and after restart it defaulted to this:

In T4168#124611, @mate-user wrote:

Setting as background should automatically save a copy of the image to /usr/share/backgrounds/solus.

This should certainly not be the case because it would require elevated privileges and it would make the wallpaper visible to every user of the machine which is something you do not want if you put personal pictures (kids, wife/husband, etc.) as desktop background.

I thought that it would put a copy of the image somewhere in the user profile but obviously it doesn't, so it's not really a bug but a feature that in my opinion could be improved. I just raised an issue here.