I have a 4 year old who loves to draw. I read on here that hand sanitizer works to take permanent markers off walls. It sure did, along with a layer of paint, but it did the job. I also tried rubbing alcohol. It didn't do anything.
The next best thing I used for my walls was SOS pads. They leave a blue tinge on the wall after cleaning but they work. It may take a few times to rinse the wall but it worked oh-so-well for me.
I hope it does for other people having the same issue with a small artist.