There is definitely no reason for a beginner to resign.
First, up or down pieces are very common for beginners. Your child can easily drop some pieces, so does his/her opponent. Picking up a free Queen is not unthinkable.
Second, a game is not only determined by pieces, but also by the deployment of available pieces. If your child's army is very active, s/he may actually be in a better position. For high level players, this is considered as sacrifice.
Third, something unexpected can happen, such as promotion, back rank mate, perpertual check, or stale mate. S/he never know what might save or reverse his/her game.
Last, and most important, playing in a down position actually trains a player to endure infavorable sitution. S/he will become much stronger with his/her mind. S/he can learn to perservere in any setbacks, survive and be the winner in the end.
I once played a young lady who was 1800. She was down a piece, and then more and more, but never resigned, until she got checkmated. From my point of view during my game, it was against sportsmanship. But nevertheless, she has zoomed up 500 points in next few years, and became a world champion at World Youth.