I am sorry for this delayed reply to your gardening question. The spring rush has brought a deluge of questions and we are working hard to catch up!
It may be due to a soil problem. Both dry soil and soggy wet soil can be deadly. Other than that it could possibly be due to a foliage/stem disease caused by fungus or bacteria and brought on by all the recent rainfall. I suggest pruning out the dead parts, fertilizing them with Miracle Gro and then watching your watering to keep the soil moist but not too wet. Disease sprays are another option but during normal weather cycles are not needed on wave petunias.
Thanks for the question. Best wishes for a wonderful gardening season. Please stop in again soon!
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