nipper-
To preserve your Eagle and keep it from "falling apart" as you say, the most important things you can do (in my eyes) are rust prevention, above average maintenance, tune ups, and thorough cleaning.
If you're serious about the rust protection, you should at least give it a good underbody spray after removing
any rust you find. Also, you ought to spray WD-40 or something similar underneath every so often. I know it is very tempting to drive such a great machine in snow, but that's one of the worst conditions for rust!
By "above average maintenance", I mean keep up with
all of your fluids and change them at regular intervals: engine oil/filter, transmission fluid/filter, front/rear gear oil, power steering, brake fluid, coolant, wiper. Also, you must keep everything possible greased so parts don't wear down as much: ball joints, tie rods, idle arm, pitman arm, driveshafts, u-joints, anything with a grease fitting. Regularly inspect components for wear, so you can change them as soon as they go bad- one bad part often leads to more bad parts.
Tune-ups will come more often than on most newer cars. Spark plugs should be replaced or at least cleaned every 30,000 miles, and inspected often for engine conditions. Other things will include plug wires, distributor cap/rotor, air filter, rubber hoses and vacuum lines, belts, and fuel filter. Keep battery terminals clean and electrolyte level up, run mild cleaners through fuel and cooling systems occasionally, and keep the carburetor tuned! These Carter carbs are known for becoming clogged, and should be adjusted to stay in top shape.
Finally, I believe it is very important to keep everything as
clean as possible. If your engine compartment is dirty, it can hide problems and prevent you from noticing them in time. If your Eagle has a plastic valve cover, I would suggest upgrading to a metal one to keep it from leaking oil. Dirt also holds moisture, which is bad for preventing rust, and can cover up weak spots in the metal.
These are good practices that will help keep your Eagle running forever. Many people have reported well over 300,000 miles on the 258 engine before rebuild. Just remember- mechanics can be easily fixed, but excessive rust can kill an Eagle!