Bug?
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When I play bughouse games, my pieces usually freeze so I can't move and it's just when I need to move the most. Then I run out of time.
Check your internet connection.
In my experience, it is not the Internet connection but chess.com programming and ads that causes movement problems.
Here's a recent, actual game that I played on chess.com. In this game, the pieces seemed to have a mind of their own (they'd go to squares where I didn't click at all):
https://www.chess.com/live/game/3358014196