I am having a very similar problem. It has been happening as long as I've had my mini. Home screen picture goes dark and very blurred (icons remain unchanged) at random times and stays that way until I reboot. I can find no relation to either app use or time. It may happen in 1 day or after 2 wks. Any help please.
Have you checked to see if the resolution size of your wallpaper may be the problem. A wallpaper for your iPad Mini should be, at a minimum, 1,262 pixels by 1,262 pixels, or 2,524 pixels by 2,524 pixels if your iPad Mini has a Retina display. That's if you use the square. It can make a difference. If you use the actual aspect ratio of the mini with Retina screen you would use a 2048 x 1536 res size. The regular mini would use a 1028 x 768 res size. A good app for sizing wallpapers is one called "Image Size". I use it all the time.
Image Size by vsmedia.de
https://appsto.re/us/oxX-N.i
The developer,Vitalij Sch?fer, is a nice guy.
Sent from my ancient but trustworthy iPhone 5. ☮