Yep - I had the same problem. Cured with a drop of CA on the "flange" of the headlight before re-inserting in the shell. Of course, now I'd better never want to get that thing out of the shell again . . . John C.
Perhaps a slightly smaller LED slipped into a cylindrical sleeve that gets CA'd to the shell. That will allow LED replacement if it should ever fail.
Unless subjected to over-voltage, over-current, or especially excessive reverse voltage (do NOT use as an LED to rectify it's own current), LEDs very rarely fail. Most unidirectional LEDs can only handle a volt or so in reverse. The wiring, solder joints, etc. may fail, but the LED won't. Now if it were a tiny incandescent light bulb, better plan on it failing, and provide for replacement.