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Newly-planted honeysuckle requires consistent watering, keeping the soil evenly moist until the plant starts growing vigorously on its own. Once established, water only during summer droughts of two weeks or more, giving the plant at least 1 inch of water a week. Place 2 inches of organic mulch around the base of the plant to reduce water evaporation from the soil.

https://www.gardeningknowhow.com/ornamental/vines/honeysuckle/honeysuckle-vine-care.htm

Treat with Neem Oil.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

There are different types of honeysuckle vine. Some honeysuckle, like lilac, is prone to mildew. Conditions that encourage mildew are overhead watering, high humidity and poor air circulation. And it overwinters in the soil so creating splash while watering starts the cycle all over. Do you prune or thin your vine? If it is vine that is non-native to your area, it may not do well in your climate. Mildew solutions include neem oil and the Cornell University Formula: baking soda, light oil, dish detergent in water. Lonicera sempervirens "Major Wheeler" is a cultivar that is said to be mildew resistant.

I believe squirrels could be the culprit. They may be stripping the bark in search of moisture (water) or attracted to the sweet flavor in the wood.

Here is more info on getting rid of squirrels: https://www.gardeningknowhow.com/plant-problems/pests/animals/get-rid-squirrels.htm

Check soil moisture levels. Has it been wet or dry? Watering issues can present themselves with yellowing leaves.
Moist or soggy soil encourages the spread of fungal diseases in honeysuckle vines. If your vine should be affected by one of these diseases, it is possible to prune your vine back as far as 6 to 8 inches to encourage new healthy growth.

Canker disease is a fungal disease that occasionally affects honeysuckle vines. This disease presents itself as a yellowing or browning of the plant’s leaves. Before the leaves of the vine begin to wilt and drop off, you may notice black spots in the form of fruiting bodies on the underside of the leaves. Untreated, this disease spreads to other sections of the vine, eventually killing off the plant. To control canker disease, always prune away dead or affected portions of the vine.
Yellowing leaves on a honeysuckle vine, also called chlorosis of the leaves, may be indicative of a nutrient deficiency. In particular, a lack of nitrogen, an essential nutrient for plant growth, is observed by yellowing leaves on a honeysuckle vine.
https://www.gardeningknowhow.com/ornamental/vines/honeysuckle/prune-honeysuckle-plants.htm
https://www.gardeningknowhow.com/plant-problems/disease/black-spot-fungus.htm

Sure does look like a nasty case of powdery mildew from the photo sent in. I recommend getting a product called Green Cure. Apply it at the Cure Rate as listed on the label. Spray the honeysuckles down very well with the mixed up spray every 5 to 7 days for at least three sprayings. That should send the mildew packing! Be sure to spray them very well being sure to get at the back of the leaves as well. Here is a link to the Green Cure website, it is an Earth Friendly product too: http://greencure.net/