I had a similar problem with my Strawberry's. Some of the older leaves were turning yellow and drying out and the roots were turning brown and looked like root rot to me. I e-mailed General Hydroponics with pictures of the roots and they told me that it looked like the
nutrient solution was getting too warm (should be between 65 and 72 degrees). Also that when the water is to warm that plants will abort fruiting and the flowers will turn yellow and fall off when this happens also. I insulated the nutrient tank and growing chambers, used pipe insulation on the return lines and add Ice to the nutrient tank before it gets warm. After I did this the roots started growing back white and healthy looking, the leaves started growing full and lush and I started getting lots of flowers.
I just mention this because you said that the plant is on the windowsill in a bottle with only about two cups of
nutrients. I am guessing that when the sun hits the bottle the water warms up. With only 2 cups of water it would warm up quite fast and be hard to control the temperature of the nutrient solution. I would also be concerned about the plant only being watered once a day.