There is an insulating disk, with a small conductor in the centre. Behind the disk there is a spring that should push the disk and conductor up onto the connection (blob of solder) on the rear of the bulb. The feed wire comes up from the rear of the fitting, through the spring and connects to the conductor in the centre of the insulated disk (plastic, or paxolin or thick card)
The springs can weaken and you also get general corrosion, also the feed cable does need to be able to move so as to allow the disk to move, pushed by the spring.
Worth spraying some silicon spray or similar into the fitting and pushing the disk (gently) with a screwdriver to see if you can work it free. Can also feel from the rear to see if there is feed wire that can be eased into the fitting to give it a bit of slack and make it easier to move with the disk.
when you push the bulb in, then you rotate it to secure it, at that point the bulb moves back out away from the disk, and the disk should follow, pushed by the spring. Sounds like the disk isn't being pushed far enough to keep the connection
May also be worth checking to see if there is any corrosion on the conductor in the centre of the insulating disk, you may be able to scrape it away with a screwdriver. Also check the solder blob on the bulb, these sometimes corrode
Ultimately its a fairly crude light fitting by Mr Lucas, the King of Darkness, they should be on the maintenance schedule to lubricate them, clean them, and check for water ingress.
