Many cars for sale now have 7 or 10-year warranties; you don’t necessarily need to buy a new car every 3 years. What it really comes down to is fairly simple: how much of a premium are you willing to pay for having a car that someone else will pay to repair? Unfortunately, the hard numbers you’d need for an objective answer aren’t going to be forthcoming until after you’ve bought the car, and depend considerably on things like your pattern of maintenance for the car, the road conditions in your area, and your driving habits.
One way to hedge your bets is to buy the car, then, after paying it off, continue to make monthly payments to a savings account. After you pay it off, there will be a period of time where it runs just fine, and then it will start to need repairs and upkeep with increasing frequency. When the repairs get to the point where you’re spending more on them than on the monthly payment, or when you have a catastrophic failure that would require a really expensive repair, use the money you’ve saved plus the car as a trade in for a new car.
Still, if you buy a car from a brand that has a reputation for durability and long life (Toyota, Honda) or from a brand that offers a long warranty (Dodge/Plymouth/Chrysler is offering a lifetime warranty on the powertrain to the original owner, and Hyundai offers 10 years/100,000 miles), you should do reasonably well.