It may help your wife to know that this statement from the Mass is a rephrasing of what Paul says about the Eucharist: "For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes" (1 Cor. 11:26).
We proclaim his death because it was by his death that we are redeemed. We had better jolly-well proclaim it—and from the rooftops until he comes in his glory!
Christ is not dead; he is risen (1 Cor. 15:12–20)! Jesus is presently alive in heaven along with all who have died in him. The sacrifice we offer at Mass is not a new sacrifice. It is the same sacrifice of Calvary that transcends all time, liberating those who lived before it and those who came after it.