The analysis problem you are experiencing is something that should be fixed soon.
https://www.chess.com/forum/view/general/stock-fish-isn-t-working-on-ios-seems-to-not-make-it-past-e4
As to a memory leak, it could very well be advertisements causing it.
Recently I have found that my computer is having a lot more trouble with chess.com. I have noticed that chess.com updated recently (see P.S.), which may have caused this. I noticed that when I was playing a game, the memory consumption started to increase over time, until my computer was having a very hard time. This is why I believe there to be a memory leak in the website. I am using chrome, windows 7.
P.S. The reason I noticed that chess.com had updated is because stockfish's suggestion is no longer free on the analysis board, even though stockfish is open-source and completely free and not the product of chess.com
. On the other hand, I guess you need to make money somehow