It's certainly possible for aircraft to be retrofitted with newer engines. One example is the [DC-8 Series 70][1], which had the older JT3D engines replaced with more efficient CFM56 engines. However, there are many reasons for this process not being more common.

There are many costs associated with changing engines. The engine may need a new nacelle design to fit the specific aircraft. This will probably require a new or at least revised strut design to mount to the wing. The wing may also need to be reinforced, as newer engines tend to be heavier. All of the systems attached to the engine, including electrical, hydraulics, and bleed air may also need changes. Avionics will also need to be updated to work with the new engine type.

Certification also should not be overlooked. Assuming the aircraft can use an existing engine that is already certified, the aircraft will still need to be certified to fly with that engine. This means a lot of paperwork with the regulators, and probably additional testing. However, engines tend to be designed for a specific aircraft type. For example, the [CFM LEAP][2] engine will power the A320, 737, and C919. All of these aircraft are similar in size and compete for the same market, yet CFM is doing testing and certification of a different version of the LEAP-1 for each of these aircraft. Each manufacturer chose to design their aircraft for a different engine version, which makes it seem unlikely that a new engine would just happen match the needs of an existing aircraft without extensive modification of the engine.

Aircraft fuselages are designed with a limited life span. As they age, maintenance costs increase as more work is required to repair damage from fatigue and regular wear and tear. Even with new engines, the airframe would still have a limited life span.

As other answers have pointed out, a new airplane design will be more efficient than just putting new engines on an old aircraft. Owners of the older aircraft would have to see a benefit in paying to upgrade their old aircraft, and having those aircraft out of service for an extended period, versus just buying a new plane that will be more efficient and will have many more flight hours left ahead of it. And some company will need to find enough of these customers to justify the large upfront costs listed above in making such an upgrade possible.


  [1]: https://en.wikipedia.org/wiki/Douglas_DC-8
  [2]: https://en.wikipedia.org/wiki/CFM_International_LEAP