Answer: There are only a few honeysuckles that aren't hardy in Wisconsin, but If yours are not hardy in your zone, chances are that the plants are stressed to begin with. A stressed plant is a target for disease and insect problems and all you can do to help is keep the plant well-watered and fertilized and hope for the best.
It sounds like you have a problem with tip blight, a fungal disease. Try cutting out the problem stems as soon as you see a leaf shriveling. Be sure to dispose of all trimmings as well as all fallen leaves so they will not reinfect the plant.
This spring, you might try to open up the shrub to more air circulation by renewal pruning. This is a matter of pruning out no more than a third of the thickest stems at ground level.
My last suggestion, perhaps more drastic, is to move the plants to a better site. Honeysuckles thrive in well-drained soil and full sun.
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