Its sounds as though your euonymus may be infested with Euonymus scale. This particularly affects evergreen species of Euonymus. These little insects clamp down upon the leaves, sucking sap from the plant and causing a pale mottling to the leaves which eventually turn yellow and drop off. Such infestations weaken the plant, causing severe die back.
The male scales are white, elongated oval-shaped, and measure about 1- 2mm in length. They generally appear on the undersides of the leaves, but it is not unusual to see them on the top of the foliage. If you take a closer look at the stems you may also notice larger, brownish oyster-shell coloured scales. These are the females. When scale insects first hatch they are quite mobile and crawl around the plant sucking sap until their hard scaly shells form, when they become firmly fixed to one spot. Males, females and juveniles may be present at the same time and they are particularly prevalent from May to August.
The best way to control this is to target the young mobile insects using a systemic insecticide such as Provado Ultimate Bug Killer Concentrate or Scotts Bug Clear Ultra. A systemic insecticide is absorbed through the foliage and kills the scales as they feed. I would also cut any dead stems back to healthy growth to encourage the plant to rejuvenate.