I don't know how much water volume that system holds, or how much you have in it. But as a general example:
using 10 gallons of water for 2 tomato plants. With that water volume and considering starting with plants about 6 inches tall. You should easily be able to go 2-3 weeks possibly even 4 weeks depending on how fast they grow. But as the plants get bigger that will change drastically. By the time the plants get a few feet tall they will be drinking up that water volume. How fast depends on how healthy they are, how much good light they get, as well as temp and humidity. You will want to replace it with plain water to replace what they drink up daily.
So if given good growing conditions the plants could be 3 or 4 feet tall within 3 weeks. At witch time you will need to either start changing the water more often like one to two weeks, or increase the water volume to compensate. In another week or so the plants will probably be big enough that you will need to change the
nutrient solution every week if still using a 10 gallon water volume. Within another couple weeks the plants could be taking up so much water and
nutrients you will need to double the water volume and still need to change it weekly.
P.S. Tomato's are continuously fruiting plants. Meaning that they don't have a vegetate stage, and a fruiting stage. They do both at the same time. Lots of plants are the same way.