One of the greatest abilities of the Fireflash aircraft was that it had the ability to fly for 6 months continuously on its atomic engines. The only problem was that they needed to be serviced every 2 hours or so to avoid radiation poisoning. With such a limited time that it could fly comparatively, what was the point of having engines that could last that long in the first place? (although I believe I read somewhere that in episodes following Trapped in the Sky that the radiation barriers were improved)
The canon quote is;
Captain : We can't stay up here for ever.
Controller : What is your endurance?
Captain : With our atomic motors we can stay up here for six months, but the anti-radiation shield needs servicing in two hours or passengers will be subjected to radiation exposure.
Since the term "endurance" specifically refers to the ability of a plane to remain aloft due to fuel constraints, the Captain of the Fireflash is telling the tower that although they have pretty much unlimited fuel, they're still going to need to land within the next couple of hours.
As to why you'd bother to develop a plane with an atomic engine that can run for 6 months but that still needs repairing every few hours, the answer is that a conventional power plant would produce insufficient energy to get the Fireflash up to its cruising speed of Mach 6