too many bikes from 1967 10s (5x2)Frejus to a Sumitomo Ti/Chorus aluminum 10s (10x2), plus one non-susp mtn bike I use as my commuter
Your description is a bit confusing, so I'm assuming that the pin is moving in and out of it's hole drilled in the chainring. It's not totally surprising as these are simply forced into an Undersized hole. Get some acetone (not nil polish remover) and wick some into the hole, or dip the ring to soak the pin. Let it dry complete, run a drop of superglue in, and quickly tap the pin into place. Let it cure overnight before riding.