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The world has lost its atmosphere. It has flown away, because the magnetic field is weakened and solar flares are making everything slowly fly away in space.
NASA has its own rockets and shuttles and all these nice things but... they do not work anymore! They do not fly, they stay on the ground, or they fly a bit and then crash.
The question is: why? Which is a possible (sound) explanation for this?
Since before 1940, there has been no plausible explanation for a failure of rockets to work in a vacuum. Simply put, rockets work better in vacuum than in thick air.
Now, your solar flares and magnetic storms that accompany them could still ground NASA and other spacecraft -- but not in a way related to the ongoing loss of the atmosphere. Rather, the electromagnetic effects of the flares are very bad for microelectronics, and every spacecraft more sophisticated than a basic sounding rocket is critically dependent on computer electronics for functions like guidance.
Without guidance, it doesn't matter that the rocket engines still work (we'll handwave getting, say, an RS-25 Space Shuttle Main Engine to operate without its electronic controls) -- the rocket can't be kept on course well enough to reach even Low Earth Orbit, never mind navigate anywhere further from the Earth. A pilot aboard wouldn't be able to communicate with ground control well enough even to manually (and inefficiently) fly a rocket into a particular orbit -- and once in some kind of orbit, unrelated to any intended mission, she'd be doing well to be able to do anything other than deorbit (that, at least, is thankfully simple: you can see your motion relative to the Earth when in low orbit, so you just need to thrust against it by an amount any astronaut going up in these conditions will have memorized).
End result: launching rockets wouldn't come to an end -- especially solid fuel rockets like most modern sounding rockets. But launching spacecraft would be done, because the computers that make it possible would all be fried.
They fly, but landing...
As @Zeiss Ikon says, rockets fly better in vacuum than in atmosphere. Getting a rocket to a set altitude or into an orbit is much easier than it was.
However, they cannot get back down to the surface of Earth without either:
To give an impression of just how bad this is - assume that a well-designed rocket that doesn't need to punch through the atmosphere can deliver 5% of its launch mass into low Earth orbit (LEO). (For comparison, the Space Shuttle could deliver <1.5% of its launch mass into LEO.) If it wants to land on an airless Earth safely, then only 5% of the payload that reached LEO can land - the rest is expended decelerating to a soft landing. So a spacecraft with a launch mass of 4,000 tons will get 200 tons into orbit, of which only 10 tons will make it back to Earth.
This assumes that all goes well - if any of the rocket firings fail during the initial launch or during the de-orbit and landing then the payload (including humans) is hamburger because, again, with no atmosphere there's no fallback option to eject and parachute to safety.
There's no physical principle that would prevent a rocket from functioning in a thin atmosphere, in fact, as others have mentioned, it would actually make things easier. What might prevent spaceflight, however, is what's known as "Kessler Syndrome." This can happen when the destruction of one or more spacecraft or satellites produces a hail of high speed shrapnel, which in turn destroys other spacecraft or satellites, producing still more shrapnel, eventually leading to the destruction of everything in orbit. With only the thin atmosphere at the edge of space to slow the fragments down, low earth orbit is ultimately filled with a cloud of shrapnel that could persist for centuries.
Realistically, this would only make staying in low earth orbit suicidal. As long as space launches passed through low earth orbit as quickly as possible the risk of collision could be minimized. However, if the scenario you are proposing is in the far-future, perhaps by that point in time there will be enough material in orbit that Kessler Syndrome would make transiting low earth orbit truly impossible. Alternatively, perhaps none of the space agencies of this setting have a powerful enough rocket on hand, or cannot afford (whether due to a shortage of material resources or funds) to build a powerful enough rocket to dash through low earth orbit with a useful payload.
There are no rockets that fly completely automatic, there needs to be at least someone to program a course and start it.
Since there was some cataclysmic event that robbed the earth of its atmosphere, all humans are dead, and no one can start the rockets.
Electrical failure
The magnetic field has weakened, so solar flares will have a larger influence on the world. One way they can do this is EMP. All systems are simply fried. If the systems aren't fried or placed just before launch, they quickly fail when they meet the now seemingly more abundant solar flares as they go up.
The design of the "bell" end of the rocket is based on the air pressure under which it is operating. Thus, rockets that operate in vacuum are different than those used for launch. You can learn about this from Scott Manley's videos on YouTube, for example. This affects the efficiency and may or may not reduce the thrust below the point of usability. And it's easy to change out the nozzle.
Rockets made for launch may also use aerodynamics for steering. Moving a little fin is easy compared to vectoring the main thrust; likewise fixed little fins are used for stability and there is no mechanism to do the kind of careful balancing needed in any other way. I think this is your best bet to be believable and understandable.
The priming and ignition systems may be tuned for or fundamentally rely on ambient pressure outside the rocket.
Rockets designed for launch stage may rely on air for cooling!
