Um, no. Unless your car is a complete shitbox to start with, or you drive ~100 miles per day every day, keeping it for 10-15 years will not cost you more than replacing it every six years. Depreciation is an accounting trick that only really works in aggregate. If your car is still running in six years time, keep it. You will save the cost of a new car. The fact that yours is worth zero on paper means absolutely nothing if it still works the way it's supposed to.
Bought a '98 Camry about 10 years ago for 8 grand. It's got 253,000 miles on it now. Off the top of my head, I've done the following non-routine maintenance to it:
Exhaust replacement, front to back: $575
Idle air control valve: $800 (Dealer because I didn't have a good cheap mechanic at the time.)
New suspension and steering parts & alignment: $800
Oil leak from oil pump: $500 (estimated mechanic cost, I did it for much less)
New air intake hose: $40
Let's round that up to $3000 in case I've forgotten a few things.
I have a car that is quiet, drives well, doesn't leak, and is reasonably comfortable. It gets 27 mpg and still has sufficient power. The money I've put in it to keep it in good working order for 10 years doesn't add up to 10 months of car payments.
Would I like a newer ride? Sure, and I may get one eventually. The fact is that I can keep this car comfortable and running for cheap money. The occasional $800 hit saves me a few thousand a year.