This has been my experience, too. I water fasted for 18 days about 9 years ago and at about day 4 I started to experience that low back pain and it kept up for about 5 days and then went away. Last week I started a Water Fast and on day 4 the same thing happened except for it was considerably worse and it extended to my thighs, too. I couldn't sleep at all and by 3:30 am I decided to quit the fast and try it again later with modifications to avoid this problem if I could figure out what to do.
I drank an antioxidant drink and after about 45 minutes my pain was somewhat relieved and I was able to sleep for a couple of hours. I noticed something interesting - when I eat it takes about 45 minutes to relieve the pain (it keeps coming back and I am in the middle of the second day of eating)and the pain stays away longer when I eat certain things and I have come to the conclusion that the pain is caused when the liver is no longer releasing bile the toxins build up and when I eat fat in a mixed meal to help slow digestion the effect lasts longer.
So how could one do a Water Fast and avoid this? I don't see how it could be done (for people who have this problem). I think a modified Water Fast with a fiber supplement and maybe a small amount of fat would be in order, and that I what I am planning to try. One time a few years ago I fasted for about 5 or 6 days taking ground flax seed twice a day, which has both fiber and oil, and I did not get this problem.