Two mistakes doomed this lawn: sodding centipedegrass in October (too late for root establishment before winter) and watering frequently and lightly—exactly what centipede hates.
Rake out dead material in May. Plug or sprig centipede into bare spots. Keep moist (not wet) for 3 weeks until rooted.

Centipedegrass thrives on neglect. Less water, less fertilizer, less trouble.
Crabgrass in New Sod: Source and Control
St. Augustine Freeze Damage: Light Nitrogen and Patience
Seeding Centipedegrass: Aerate First, Then Sow
Establishing Centipede Grass: Seed vs. Sod After Winter Rye
Centipede Grass pH at 6.5: Should You Lower It?
Repairing a Lawn Destroyed by Large Dogs
Fixing Poor Grading and Water Pooling in New Lawn
Schefflera Losing Leaves: Root Rot, Cold, or Disease?
Coca-Cola on Centipede for Thatch: Myth, Not Method
Accidental Weed Killer on New Sod: Assess Damage, Spot-Repair
Torpedo Grass in St. Augustine & Endless Seed Heads: Organic Rescue Plan
Rescuing a Chemically-Dependent Hamptons Lawn: Organic Rehabilitation
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