Did the insert come loose from the cap, or did the screw that went into the insert come loose? Either should be able to be replaced. If this screw is also the axle the shade rotates on as it goes up and down, depending on how the shade attaches to the frame, you may not tighten the screw all the way down. It may take a tiny drop of loctite to keep it from backing out. It would be different if the insert was the axle, in that case the screw would come go through the cap from the inside and the insert thread on the outside. If the inset is the axle I bet the screw would be tighten down. Again, if it's working itself loose, a bit of loctite would help. You may even see a bit of blue or red residue on the threads if it was done at the factory.
It's really hard to know from your description without seeing the shade and frame.
If you need a new insert a lot of hardware stores carry them.
Tom M. 1998 Safari Serengeti 3706,
300HP Cat 3126 Allison 3060, 600 watts of Solar.
Fisher and Paykel Residential refrigerator