My understanding is that it has to do with the "chemistry" of DI water. Apparently, water is a pretty aggressive solvent. Many minerals dissolve upon contact with water. These are the minerals that you find in tap water and that you are trying to take out in the RO/DI process. The tap water you drink already has a large amount of minerals and such dissolved into it and thus isn't as "hungry" to dissolve more; it doesn't have the potential capacity to continue dissolving more. What is left after the process of RO/DI is an unusually pure form of water. When this water enters your body, the fear is that the water will attempt to dissolve minerals, etc. from the only place it can: your body. In essence, it may act the opposite way of taking vitamins. Instead of providing vitamins and minerals for your body to absorb, it "sucks" these vitamins and minerals from your organs.
Many people argue that they have been drinking such water for years without consequence. But of course, one would think that the slow depletion of vitamins from your body would not necessarily have immediate affects, especially if they were being replenished as quickly as they were being taken out by the water.
Another problem cited is that the DI resins are a good breeding ground for bacteria. I don't know about you but my RO/DI has been set up for years and I only change the filters when the readings start showing dissolved solids. That is months.
Finally, from a practical standpoint, it is the minerals in water that gives it its taste. From what i'm told, the tastiest water is the water coming out of the waste water tube, not the purified water.
For me, I just don't see any reason to use myself as a human guinea pig to determine the long term affects of drinking DI. What is there to prove? It doesn't have any taste, it may be harmful. In this age of thinking that everything has to be "green" and pure, it may seem logical to assume that the cleaner the water, the better it must be for you. However, our bodies weren't designed to live in a laboratory. They are designed to live in nature where water has minerals, etc.
FWIW