This looks like Phytophthora root rot. With Phytophthora, you will see wilting and dieback of canes in early spring to late summer. The leaves of infected canes will turn yellow or bronze, wilt, and die, and the dead leaves stay attached to the cane. The primocanes (this years new canes) will usually wilt from the tip down. To diagnose this disease, examine the roots of a dying, but not yet dead, plant. If the bark is scraped from the main roots and crown, and the layer underneath is white, then it likely isn’t Phytophthora. In Phytophthora infected plants, this layer is red-brown, and will later become dark brown. Often there is a distinct line where the infected and healthy tissue meet. This is an environmental problem usually due to heavy soils with poor drainage that leads to the roots standing in water. The raspberry plant will eventually die from it. Don’t replant in the same place and be sure the plants are in well-drained soil. The fungus spreads from plant to plant through the spores that move through water, so you need to prevent puddling or flooding around the plants.

There are other diseases to consider, such as Verticillium wilt which will also cause wilting and dieback of canes, but you typically see the symptoms appear later in summer, the wilting usually starts at the bottom of the cane and moves up (so leaves on tips of canes initially stay green), and the wilted dead leaves will drop prematurely. Fruiting canes may take on a bluish black cast and die during summer as fruit are maturing. Verticillium is more serious in black raspberry compared to red or purple raspberry varieties.

Armillaria Root Rot also causes similar symptoms. The first visible disease symptom is a decline and dieback in which leaves turn yellow, wilt, and die. This may occur only on one side of the plant or in one or two canes. You can diagnosis this by digging down about a foot below the soil line and use a pocketknife to remove thin layers of bark from the root collar. Mycelial fans are thick, white layers of fungus that adhere to the root bark and/or the wood beneath the bark.

There are also several cane blights that effect raspberry. This is unlikely unless the raspberry canes were damaged last year. A fungus invades wounds on canes stubs or pruned canes. You can read more about the various cane diseases and their symptoms here.

Based on the symptoms I can see in the photo, and the timing of symptoms, I do believe this is Phytophthora, but laboratory testing would be needed to confirm. You can send a plant sample to the OSU Plant Clinic in Corvallis for a diagnostic test to confirm the issue. Phytophthora, Verticillium and Armillaria are all soil pathogens that will eventually kill the plants. The general recommendation is to remove infected plants, and do not replant raspberries or other susceptible plants where the infections occurred. When planting new raspberries, purchase certified disease-free planting stock and look for resistant varieties. The links provided above will also list additional management practices and recommendations.