Quick answer: Renew the COE when the car's condition is good and the renewal cost is materially lower than buying a comparable replacement after expiry. Deregister when the existing car needs heavy work and the PARF + COE rebate is worth more than selling. The decision depends on (a) prevailing COE premium, (b) the car's market value as a renewed-COE car vs its paper value, and (c) the car's mechanical condition at expiry.
When your COE approaches expiry, you can renew it for 5 or 10 years (at the prevailing COE premium), deregister and collect the rebate, or scrap / export. This decision matrix helps you compare the numbers.
Renew makes sense when the car's condition is good and the renewal cost is materially lower than buying a comparable replacement after COE expiry.
Deregister makes sense when the existing car needs heavy work, the market value is low, and the PARF + COE rebate is worth more than selling the car.
Sell before expiry makes sense when you can find a buyer who values the remaining COE time and you would rather exit than commit to a renewal decision.