Dear John,  I know how upsetting it can be when a favorite plant takes sick.

Daphne plants are particularly fickle.  While I research, there are some questions 

 that I need the information/answers to hone into your problem/sick daphne plant:

How old is the plant. When was it planted, transplanted?

What is the exposure. Full sun— full shade

Soil type. Loam -clay

Watering, over head sprinkler, drip, soaker hose, hand. Frequency

Fertilizer? What type & when if any

It looks like you have several daphne plants, Is this problem limited to one individual. Are you seeing any signs on other plants in your garden?

When did you first notice a problem and has it spread and how fast

Is the problem on only part of this individual plant. Please describe.

Have you looked for any insects or mites.

Have you tried any treatments or remedies? If yes what and when and result.

I haven’t received any response to my queries, so I’ll send a brief overview about daphne odorata.  

Daphnes require slightly acidic soils that are moist (not soggy) well drained soils. Once planted they do not like to be moved. They prefer morning or dappled shade. Yellow drooping leaves normally signals overwatering and root rot issues.

Potential diseases include botrytis, leaf spots, canker, twig blight, crown rot, root rot and virus. Potential insect pests include aphids, mealybugs and scale. Plants can be temperamental and unpredictable.

I suspect it has a root rot based on the photos but this is purely conjecture. If it turns out that the daphne does die, don't plant another daphne, or other plant susceptible to root rot, in the same spot and keep a close watch on the daphne next to it.

The more common longevity for a daphne is 10 years. And according to Michael Dirr daphnes sometimes die very quickly for “no explicable reason.” 

The plant is about 6 or 7 years old. I see no insects. It is shaded by a cherry tree on the west side of the house. No other plants seem affected. This just happened all of the sudden. We water it slightly a couple times a week . Being that it is shaded it doesn’t dry out too much. If it’s root rot, how can I try too solve this? Thank you for your advise!

The plant is about 6 or 7 years old. I see no insects. It is shaded by a cherry tree on the west side of the house. No other plants seem affected. This just happened all of the sudden. We water it slightly a couple times a week . Being that it is shaded it doesn’t dry out too much. If it’s root rot, how can I try too solve this? Thank you for your advise!

It is impossible to know what exactly is causing this sudden collapse without laboratory tissue testing. In the photos the leaves are curling down and yellowing and the growth tips are atrophying   Which is why I suspect a root problem is preventing water transport to leaves.However in researching several sites and problems for daphne they recommend the same cultural practices as the main control:

• Improve water drainage around plantings.
• Reduce irrigation amount and frequency.
• Maintain at a slightly acidic pH and do not over-fertilize with nitrogen.
• Remove and destroy infected plant and potting material including leaves, cuttings, plants, and potting media.  

Chemical control: Focus on cultural controls. If using chemicals, Use fungicides as preventative treatments. to prevent the spread to other plants. Fungicides can only prevent establishment of the organism before it gets into the plant. They can also prevent continued growth if the organism is already inside the plant thereby delaying symptoms that might have developed. Once chemical activity has subsided with time, the organism can resume growth within infected plants.  If you do decide to use a fungicide, be sure to read the entire label and follow its directions.  
I am known to stand in the aisle of a horticultural store to read the label to make sure the particular plant I want to treat is identified. Or I have looked up that particular product online to read the label.

Please remember somethings are beyond our control.   And daphnes sometimes suddenly collapse for “no explicable reason”