Repairing a boom lamp that keeps falling
It sounds as if the knurled knob loosens over time. There are a number of solutions.

The knurled knob seems to be either the head of a bolt or a specialized nut. In either case, a washer between the knurled head and the body of the lamp arm may help. A flat washer may be enough.

 

If not a lock washer should help.



Another approach is a locking fluid spread on the threads of the bolt that prevents loosening, such as this stuff.



There are different versions, depending on whether you want it to be removeable or permanent.