Damping-off is always a possibility with germinating seedlings, not just of watermelon, but of many plants. In watermelon, the disease is usually caused by Phytophthora or Pythium fungi. The disease affects the cotyledons (seed leaves) and causes the collapse of the seedlings when the stem is girdled. Signs to look out for include a watery rot on the seedling at the soil line. The development of damping off is favored by cool, wet conditions which slow germination. It can be prevented by avoiding the overwatering of plants and planting in raised beds or on ridges.
Do your watermelon plants have specific symptoms you can share with us? Some images would also be very helpful for diagnosing the problem.