Annual sunflowers (Helianthus annuus) that grow in containers are very susceptible to drying out. Most are big plants with big root systems. When you cultivate them in containers, keep the potting mix slightly moist at all times. Remember that the plants can't send their roots deeper into the soil; they rely on you for their moisture. If they don?t get enough water, their leaves may turn crisp. If your sunflowers require more water than you can supply, grow them in larger containers. The smaller the container, the more you'll need to water. It also helps considerably to site your sunflowers where they are protected from the wind (plants lose a lot of moisture through their leaves, especially on hot, windy days) and where they get a little shade during the hottest hours of the afternoon.