If the notify icon is logically tied to this instance of the form then you shouldn't have it be a static field. Marking it as static is done to specifically say that it's not tied to one instance, but rather is shared between all instances.
I would think that when the form everything else gets destroyed and freed up?
If it were instance data it would be, but because it's static, and therefore not tied to the instance, it will not be cleaned up when the form goes away.
Of course, if this is the main form (and not a misnomer) then the entire application will end when the form closes, which will clean up everything regardless, static or not.