Can you show a more detailed picture of that round metal knob, and a picture of the bare handle the cover goes onto and the knob goes into?
You may be able to wrap the bare metal handle with something that will stick to it but preferably without adhesive that will leave a residue if it doesn't work. I'm thinking something like Teflon comma though then you would have to put something on it so the handle doesn't just slide right off. But something to thicken the piece that the black rubber grip slides onto so it's tight when it goes on.
Then you might be able to use something like J-B weld on that round metal knob and well that into the metal handle which should then hold the rubber grip on.
Basically if you can get that round metal knob to stay in place it should hold the other one in place. Then even if you wrapped the bare metal with Teflon to thicken it up, the rubber grip would rotate but it wouldn't slide off and it wouldn't be loose.
That's how I would go about troubleshooting that. But I'm just guessing at how the handle and grip are assembled without more detailed images.