Driving a car until the wheels fall off generally doesn't make financial sense. Keeping an old car on the road gets really expensive unless you have the space, time and skills to do all the work yourself. Then there is the opportunity cost of not having access to your car for days/weeks at a time while it is being repaired. Finally you have the stress of not being quite sure if your car will start when you turn the key or get you where you want to go.

From both an economic and quality of life point of view, you are better driving your car until it starts to get slightly unreliable and then quickly trade it in for a slightly newer used car. Buy a 5-10 year old car, drive it for 5-10 years, then trade it in for a 5-10 years old car is probably pretty close to an optimal strategy.