An ice dam is the symptom. The disease is a warm attic melting snow off the field of the roof, which then refreezes at the cold eave and backs water up under the shingles.
The permanent fix is not more heat cable at the gutter. It is better attic insulation and better attic ventilation, so the deck stays cold and the snow stays snow.
In a serious ice dam winter, ice and water shield installed up higher than the code minimum on the last replacement is what saves the ceiling below.