My eshopps has a similar design where you can't clean inside the bubble plate. I ran my skimmer in a water/citric acid mix and it cleaned it right up.
But as for cleaning the body of the skimmer, I clean mine once a year or whenever I clean the pump for it. There shouldn't be a "break in" time like when it's brand new and keeps overflowing. You may have to adjust the skimmer a little bit as the biofilm builds back up on the surfaces.