Your FEN (you can see this by downloading the game) is missing the Castle permissions.
[initialSetup "brkbrnnq/pppppppp/8/8/8/8/PPPPPPPP/BRKBRNNQ w - 0 1"]
That's why the game won't let you Castle. The question is how the game started with that FEN and my guess is the iOS App is not making the games correctly.
Just as sushi_rice, we do rematches all the time. I sounds plausible that iOS messes up the setup of the game.
Is there any way to fix the castling on the running game?
I experience the same castling problem behavior. I have played hundreds of Chess960 games (I know how it works), however recently both me and my chess opponent cannot castle anymore.
https://www.chess.com/game/daily/292221044
The browser doesn't work, the app returns "Illegal move". In the analysis it allows the move.,
Did you happen to start these games on iOS's APP?
My opponent started it from the iOS app.