What is causing my newborn to have hiccups all the time?

Unknown! The cause of hiccups is unknown. Muscular activity of the diaphragm is controlled by nerves and hiccups occur when particular stimuli trigger the nerves to send the diaphragm into spasms. We do not know why this happens. However, they are are common in babies, harmless and usually resolve by themselves after a few minutes.
Tickle the diaphragm. Your baby's stomach is very tiny to start with, it also sits right under your diaphragm. When baby eats or swallows a little air, and the stomach enlarges, it can actually "tickle" the underside of the diaphragm, and then hiccups ensue! Take it as a good sign that your baby's tummy is full, or he needs to get another burp out. Remember, hiccups bother you much moe than they bother him!