This study also found dates being effective in preventing postpartum blood loss. Those women eating dates immediately after delivery lost less blood than those receiving Pitocin (a drug often given preemptively in hospitals to prevent hemorrhage). The calcium, serotonin, tannin, and glucose in dates are thought to have roles in slowing the bleeding.
I also would recommend dates in the last few weeks of pregnancy because the glucose (sugar) in them is the body's main source of energy. Muscles need glucose to function most efficiently, and the uterus is a large muscle, after all. Getting more carbohydrates from natural foods as labor nears can help you, especially in a long labor. If nothing else, dates might be a welcome healthy sweet treat after months of watching your diet!