The connection between the battery and the light on my Ay-Up lights (https://www.ayup-lights.com/) had worn out - if the plug was nudged or turned the light would go out. I figured the problem was probably on the battery end because one of my batteries that I use much less frequently does not have the problem. The batteries are way out of warranty. I bought these connectors: https://www.mouser.com/ProductDetail/...ebNsunJWNfDh6A and soldered them on after cutting the old ones off, and added some shring tubing and superglue for water resistance. The connection feels more solid than the old ones. They are a bit bulkier without the bend of the old connectors. $5 instead of $60+s/h for a new battery.

The connection on my AYUPs is a bit loose too, not as bad as yours though. Mine will work itself loose after a couple of days of riding (on road bike on sealed roads). I have my plug joining the light from the bottom for a neater look, maybe this is part of the reason it comes loose. I've had a couple of different lights and a couple of different batteries and they've both done it. Good lights apart from that. I might order some of those connectors and see if that solves the problem.