dotken, you really shouldn't need more supports. Several of us have had the same problem I assume you may have had. The rod came down??
It helps to have a stud finder but try to locate the framework of the shelf above the closet rod. Align the support on a frame member and using a 1/4" drill bit, drill up through the shelf/frame. Use carriage bolts and large fender washers down through the shelf and support and secure with 1/4" nylock nuts. This should prevent the rod from falling again.
The problem is caused by 2 things. The factory doesn't pre-drill the holes for the screws used to hang the supports causing the pine to split & weaken. Sometimes the factory misses the framework with the support screws.