I find that long fasts are preferable to short ones because once the body is in the fasting state it cleanses systematically into the harder to get at body tissues. For this reason, most of the recoveries from illness have taken place in the latter parts of long juice or water fasts. A friend's hemorrhoids were healed on the 21st day of a juice fast after suffering from them for 15 years.
Long fasts give the body the uninterrupted time to do the work of healing.
I compare it to getting a piano tuned. A piano tuner can tune a piano in three short visits or one long one. Three shorter visits will take more time and energy because he has to drive back and forth, loading and unload his tools. The first few days of fasting gets rid of the gross waste products of digestion, but only after this can the body pull out its tools to get to work on healing. The thirty day juice fast is a standard in European health facilities.