In recent years, the nets have become a leading method of preventing malaria, especially in Africa.
In the last 4 months of the study, the researchers found that malaria attacks returned to high levels.
Among older children and adults the rate was even higher than before the introduction of the nets.
Other experts however say the study was too small to draw conclusions about the long-term effectiveness of nets.
The researchers argue that the initial effectiveness of the bed nets reduced the amount of immunity that people acquire through exposure to mosquito bites.