That's interesting...right-clicking is how you turn it on/off. Try opening up your abilities list and make sure that "Lock tray" is unchecked. I don't think that would make a difference, but it's worth a try.
make sure you are right clicking on the box that shows all of your weapons together, and not the power tray.
I have tried clicking wherever I can click, but nothing seems to help. That and the fact that I cannot turn it on, on my other weapons (which I do not mind since I don't want to have them set to autofiring)
Let me resume. I have three aft weapon slots, a faser, a torpedo and a mine lancher. The middle is set to autofiring. If I swap the faser and the torpedo, the faser is set to autofiring, when I put it on my action bar. When I swap the mine lancher with the faser, that is set to autofiring. Also, it can only be seen on the icon on the action bar.
Since I fire my fasers with the space bar, I don't have the faser icons on my action bar. So I put the faser in the middle aft slot. This way it looks like my weapons are on standard (as I want it) non-autofiring,
I am also not aware if it does auto fire, since my right hand seems to stand on auto hitting the space bar whenever I am in combat.