What's the TDS of your tap water?
Can you take a picture of your unit (oh that sounds bad!!

), or provide a link to your exact one? As hillegom pointed out, I'm wondering if you have confused the DI cartirdges for particulate and carbon filters. The order should be: particulate, carbon, RO, DI. Once the water passes through the RO it should not be greater than 20ppm or it will exhaust the DI resin very quickly, and will not get it down to 0 ppm TDS. Try disconnecting the hose feed between the RO and the DI and test the water coming out of there (collect it in a clean cup for ease of testing). If it is greater than 20 ppm or approaching 20ppm I would suggest you add a second RO cartridge. This would probably only be a problem if your tap water has really high TDS which is very possible where you live.
EDIT: You have a 7 stage filter system? There is no reason to have a system that large for tap water with a TDS of 50 ppm. My tap water is 90-95 ppm, and my 4 stage (particle, carbon, RO, DI) gets my product water to 0 ppm TDS. I am wondering if your adjustable flow restrictor is faulty...I have never seen one of those before, and I am leary about how it may work.