A little ohms law related thinking is warranted here. Turbo Turbine is onto the source of the problem but is a little off in the theory explanation.
When a particular pin is loose or foreign matter is causing a poor connection, this causes resistance to current flow at that point. Any time there is resistance to current flow, the energy is dissipated as heat. Because there is resistance to current flow, there is LESS current flow, but the energy is being dissipated at the bad connection, rather than all of it being dissipated as light and heat at the bulb filament.
Replace the socket and make sure you make good splices, if not, there will be resistance at the splice, causing the same thing to happen at the splice.
Have a great day,