But some designs defy obsolescence
This isn't about obsolescence or a design that stands the test of time. This is about simple economics. The main reason airliners phase out old airplanes is that their operating costs are too high - their older engines are too fuel consuming compared to newer designs, and may not meet newer noise regulations for most commercial airports. Maintenance also becomes difficult to source with no new spare parts being produced.
Fire fighting aircraft fly under a different set of economics. They fly short flights, and only seasonally, so their fuel expenses are a smaller proportion of their expenses. They don't have to worry about noise regulations, because they don't fly out of commercial airports. And an older model that was produced in large volumes like the DC-10 means there is a large source of cheap junkyard parts to maintain these aircraft.
This isn't about the DC-10 being a good or bad design - it's just simple economics. What's expensive for a commercial airliner can be economical for a fire-fighting operation.