You could replace the rivets, but the holes are probably enlarged from corrosion, so new rivets might not work too well.

There should be three rivets - one on each side and one in the front. If the one in front is missing, you could pop one in there and tighten it up.

The only time that the rivets are even stressed is when you step the mast. When sailing, the mast is under compression. When you step / un-step the mast, the rivets are under shear as the base tries to pivot off the mast extrusion.