When you sail, the stern wave is pumping water up and thru a leak somewhere.

We had something similar happen when the lip seal in our lower rudder bearing got damaged. But I doubt you have a lip seal in there.

Looks like it may be a delrin sleeve bearing inside the bronze piece, but its a bit hard to tell from the photo.

Take it apart and you will find out :) and inspect the rudder shaft while you have the opportunity.

If it is a delrin sleeve, most machine shops could make a new one - mine is UHMW plastic rather than Delrin because it absorbs less water.