Are these slotted pins?
First, make sure that the ball of the string is not pulling the pin out as you tighten the string... Most of my pins have a bevel on the end, so that the string ball cannot catch the end of the pin and pull the pin out when I tighten the string. Even so, before starting to tension the strings, I always give the spring an upward pull while holding the pin in place, to make sure the ball and pin are correctly seated.
The 6th string (bass E) is the fattest string, and sometimes as you tighten it, the windings act like little ratchet teeth against the pin and cause it to rise out of position. If this is what is happening, you can just GENTLY push the pin back into place. DON'T FORCE IT! If it doesn't seat with gentle finger pressure, it is too tight, and you might split the bridge. If it is too tight, you can try and file the pin slot a little... or use sand paper to reduce the diameter of the shaft a little...
...but before you do that, just try swapping the pins around. Sometimes the slots are not identical, and you can find one that works better with the 6th string. IF that works, you might consider marking the bottom of the pin shaft with a sharpie, so you can tell that it's "special."
