What limits the lifetime on the F-16 airframe? I assume it is material fatigue, but what kind, and where on the airframe?
Moreover, what exactly happens? What will happen if this problem is ignored? Will the wings break off? Will the airframe collapse or break somehow?
What can be done about this problem? Can the airframe be maintained somehow, repaired, replaced? For how long can this be done, indefinitely, or only up to a point where it is financially feasible?
It is difficult to estimate how long a particular airframe might last. Also, different aircraft might last different amounts of time for esoteric reasons. For example, mercury amalgamates with aluminum and can weaken it. Even a small amount of mercury can significantly weaken an aluminum structural member. Therefore, you might have one plane with some mercury contamination that will not last nearly as long as one free from that accidental contamination.
Also, how the aircraft is used will significantly affect its lifetime. A few high-stress maneuvers can weaken an airframe. Conversely, an aircraft that is babied and lightly driven may last for many decades.
Ultimately, there is no way to predict how long a given aircraft will last. The best thing to do is to observe it and when cracks start to appear, then you know there is a problem.
To compensate for fatigued structural members, it may be possible, but it depends entirely on the scope and nature of the fatigue. If the fatigue is limited to a restricted location, then theoretically that area could be reinforced. The problem is that the complexity of the engineering is such that in most cases it will be cheaper and more effective to simply replace the aircraft.
Usually wear is most severe at the wing roots, so a plane that is experiencing fatigue can potentially be improved by replacing the wings, but the cost of this is pretty significant, so normally you would only see this in an air force that could not buy new aircraft for some reason.
All military aircraft have airframe time limits, and they are mostly related to fatigue. It should be easy to figure out what portions of the airframe are stressed the most -- think of what sticks out the most from the center, and what's connected to that, or what is subject to stress every time the aircraft flies even if it just goes around the patch and lands.
In reality what aircraft manufacturers will do is mount the aircraft or components thereof in testing fixtures and subject them for long periods of time to the types of stresses that they will have to handle in operational situations. For example, airliner wings are mounted on fixtures and subjected to random stresses with hydraulic actuators. They also have to perform tests that test components to the failure point to confirm what engineers thought it would be.
Some airframes can be overhauled and made airworthy again after they have reached their service limits. The USAF is doing that with some 300 F-16 aircraft in Utah. However, that will only add 4,000 flight hours to the service life of the fighter, or 50% of the original 8,000 flight hour service life. Some customers may look at the cost involved in doing that and decide new aircraft are a better deal.