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I have several almost new 2102-D's as many were available on eBay for $5-10 at one time. An easy fix for loose center pins is to apply the tinyest drop of Cyanoacrylate glue at the pin/hole joint. CA is sold in hobby shops (model airplane builders) and comes in various thicknesses. Unlike the 'thick' CA which is designed to be gap filling, the 'thin' suff is designed to wick into micro-cracks and it bonds nicely.

When working with CA, you mate and align the parts first, then apply the adhesive to the joint between the pin and the star finder plate. It's best to dispense thin CA only from the tiny plastic tube dispenser that is packaged with the glue bottle. Do not try to dispense it directly from the CA plastic bottle as you will most assuredly put too much on. It helps to let a tiny drop form on the dispenser tube and only let that drop touch the 2102-D's pin/hole. For applications where you absolutely do not want to chance having CA wick beyond the tiny working area, apply it upward (against gravity) to the affected parts and not down where gravety may cause it to flow beyond the intended area (make sense?). This means holding the 2102-D up and applying glue from beneath.