I haven't been keeping up with this research, but 10 years ago astronomer Jack Eddy looked into this using old sunspot observations by Galileo and other 17th century astronomers. I think the bottom line was that no significant shrinkage had been detected...but I cannot be certain. It all seems to be tied to the magnetic field of the sun, the thickness of the sub surface convection layer and other things which may cause slight radial changes...but gains and losses seem to be roughly in balance to that the net solar output has not changed by more than a percent or so in recent human history.
All answers are provided by Dr. Sten Odenwald (Raytheon STX)
NASA IMAGE/POETRY Education and Public Outreach program.