Certified GKH Gardening Expert
Japanese willows need quite a lot of water. You can also trim them a lot to keep them nice looking. This article may help
Is this a new planting? This does sound like a watering issue. New plantings should be watered daily for the first 2 weeks.
After that water each week with slow and deep watering.
Add 3 to 4 inches of hardwood mulch but keep it about 6 inches from the base of the shrub.