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.