I just dealt with this issue when replacing the bar-end weights on my Italjet, and have had the same problem with my bar-end Napoleon mirrors on my T3.
The mounting screw engages with a device that sits in the smooth inner bore of the handlebar and then expands when the screw is tightened. Though there is more than one kind of these, they are all subject to being displaced when the screw is taken out. After that happens you won't be able to engage the screw any more.
The solution to the problem is to withdraw the device from the tube, thread the screw into it, and re-insert.
In the Italjet's case, the device is essentially a drilled rubber stopper with a nut inserted on the far end. The stopper has been cut through on a diagonal so that the screw will pull the two halves together when tightened and cause them to become offset, thus gripping the inner bore. I also considered whether I needed to remove my handlebar grip, but looking more closely I could see the end of the handlebar tube, and the rubber stopper sitting inside it.
If you can see a drilled rubber stopper as you look in the end of the bar, try prying it out from the edges with a small screw driver and then tugging and wiggling it persistently with needle nose pliers. Once it's out, you'll see the solution easily enough. You may need to fish out the loose nut if it is no longer attached to the rubber stopper.
I don't remember the device in my Napoleon mirrors, but the principle is the same: remove it, rethread the screw, and reinstall.
Hardware stores sell such devices (I forget what they call them), but you've got one in your bars, and just need to get it out.
EDIT: Here's a photo. The original bar-end weight at the bottom has its screw threaded through the split stopper and the seated nut at the end of the stopper. All that remains is to insert the whole business and tighten it up.
EDIT #2: I took the opportunity to glue the nut into its recess (with Duco Cement) to make it harder to dislodge in the future. I also began rotating the screw while it was still in the rubber of the stopper, rather than pushing it through, in order to avoid such a dislodging. But you'll figure it out. Good luck.