Answer: Black walnut (Juglans nigra) has a reputation for being allelopathic--that is, for inhibiting the growth of other plants. Small amounts of a substance called juglone are released by the tree roots, but a far greater amount of this growth-inhibiting chemical is found under the canopy of the tree.
Bleeding heart is sensitive to juglone. Some plants that are tolerant include: arborvitae, cedar, catalpa, clematis, daphne, elm, euonymous, forsythia, hawthorn, hemlock, sycamore, astilbe, begonia, bellflower, orange hawkweed, hosta, pansy, phlox, marigold, primrose, snowdrop, sweet woodruff, trillium and zinnia. Since your walnut tree is there to stay, try to plant one of the less-susceptible plants in the vicinity of the trees roots or canopy.
And, if you relocate your bleeding hearts to another shady area, they'll probably perk right up!
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