The problem with aerogarden and nutrients

Heyo. I have heard several places that people are having trouble knowing how much nutrients they should add to the water in the aerogarden. The plants drink, and you need to add more water, but don't know how much nutrients you need because you don't really know how much nutrients is left etc.
So anyway, my question is basically, wouldn't it be easier to fill a large barrel with water and enough nutrients, and then, whenever you need to change water, you just fill up from that barrel? I'm guessing this would make the water have a perfect amount of ppm at all times.
Or do i miss something?
Oh and another thing, if this is a good idea, how long can the water be staying like that? Will the nutrients diminish over time (say 2 months), or will that long time have a bad effect on the water?

Make sure you use liquid nutrients for the AeroGarden. There are some good ones at www.hydroponic-home-garden.com or www.igardenshoppe.com. You can't just create a whole barrel of nutrient water, because you'll need to adjust the amount of nutrients, and proportions of each type as your plants grow. It's actually really easy to do. Instructions for mixing are on the bottles.