Puzzling move... and test
I was looking at a puzzling move and also wanted to play with the Board Analysis and Editor feature (the move is 30.f6 -- the game below did not keep the Focus position or highlight the move as marked in the editor before pasting here). It didn't keep comments either, like it did in the Embed function...
...I did include Test in the subject of this post. I am new to Chess.com as a paid member and was hoping that analysis could be saved such as to a personal folder/game list. The best I've found so far is to Copy PGN and save it elsewhere, or to copy the Embed text and place it in a simple HTML page where it can be viewed and played through, and by clicking Analyse, you can even return to the Analysis Board and Editor to continue.
By the ID (game?) number included in the Embed text, I assume that Chess.com does save the game/analysis, though I don't know for how long.