This is the thing to look at if your product water is reading anything more than "0" TDS by conductivity. There are multiple gaskets in a typical RODI system that can become displaced in shipping and/or assembly. One of the more common issues is a displaced RO membrane gasket within the RO membrane housing, which leads to very rapid exhaustion of the DI cartridge.
I'd recommend checking the gasket installation as Buckeye suggests; I'd also recommend picking up a small container of pure silicone grease from the home store, and very lightly lubricating the gaskets before reassembling everything. You want to just "color" the gaskets with the grease, with no excess - it really helps to prevent gasket distortion/displacement.
One other thing to check is that your DI resin hasn't developed a channel. It's pretty easy to pour out the resin into a measuring pitcher, suspend it as a slurry, and pour it back into the resin housing to ensure a good packing (and that RO water isn't bypassing most of the packed bed by going through a channel).
Presuming you're actually the guy from TV, thanks for taking on the science-education task. Many of us with science degrees don't have the time (or possibly inclination) to do so, but recognize that it's a critically important task, particularly for young people.
