We had a similar problem with some of our kittens last year. Three rescued feral babies with chronic diarrhea Two were using the box well, but the third would pick a spot (not in the box) and go She also had a leaky, butt. It's like her sphincter didn't work well. She would walk all over the house dripping diarrhea; and if she lay down, there would be a puddle of the stuff . It also kept her hiney very icky. I was cleaning up poo spots forever, until we figured out who it was.
We put the kittens in a ferret play pen and tied another pen panel on the top to keep them in. I also put newspaper in the bottom of the pen to make clean up a little easier; since the one was still drippy. When I would clean the pen, I put the kittens in a carrier so they wouldn't tack poo everywhere.
The vet finally determined they had Tritrichomonas foetus. This was after three other medicines/wormers didn't clear it all the way up. The medicine had to be special ordered, but it worked. And the little kitty uses the box, now.