To go by the board means to get ruined or lost, but in this sentence the speaker is saying that the thing won't get saved or preserved
Consider the staetement "He spoke then more to keep up his own courage than to argue: This isn't the kind of thing they'd let get saved or preserved.". Based on this statement, is "He spoke then more to keep up his own courage than to argue: This isn't the kind of thing they'd let go by the board." a true statement? Yes/no/unknown