I think that 3 day rule only applies to straight water fasting. Even then many experienced fasters are comfortable doing long fasts on their own. Juice fasts aren't that big of a deal and if your concerned just check in with a doctor, preferably one who is open to the idea, every few days.
People seem to forget that "juice fasting" is not actually fasting. You are taking in nutrients so the body doesn't undergo the same changes it would during a water fast, such as shutting down digestion and going into hibernation mode. With that said, juice fasting is a great detox and weight loss tool. It's also a very useful for the folks that don't have the time to Water Fast due to life and work.