At what age does a regularly maintained airframe most commonly start needing frequent repairs?
Not an aircraft owner here, but based on the AOPA article Tips on Buying Used Aircraft, the one thing that stands out is to negotiate a much lower price if the aircraft is close to its time between overhaul (TBO).


  [Let's say] you are purchasing a 1977 C-172N for \$40,000. The TBO for this aircraft is typically 2000 hours, and costs roughly \$20,000; or half the value of the aircraft. If the aircraft you are considering buying has 1800 hours on the engine, you need to expect to spend an additional \$20,000 on the aircraft in your first 200 hours of ownership. Knowing this, it would be in your best interest to negotiate a lower price for the aircraft.


Depending on you where you will be flying, you may be required to install ADS-B by Jan 2020. If the aircraft you are buying is not equipped, then that's something to add to the list of things to buy. (What is ADS-B and who needs it?)



There are also these related posts:


What are the typical facets of ownership costs, for a single engine aircraft?
Is there any limit by FAA on the age of aircraft to be operational?