Being in check means it’s your move and the pieces are positioned so that if it was your opponent’s move they could capture your king. So, to “remain in check” would mean to make a move which still allows your opponent to capture your king. If this were allowed the opponent would just capture your king and you would lose. Instead, the rules of chess require you to “get out of check”, i.e. make a move which prevents your opponent from capturing your king. If there is no such move you are said to be in “checkmate” and you lose.
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