Well don't forget that how long the processor survices depends heavily on the shielding, for example on the ISS the astronauts use standard IBM Thinkpads with Windows (I heard they had a macro virus on them at one point).
On the other side of the spectrum the mars rovers are running VxWorks on a MIPS compatible processor (33 Mhz) but still thanks to a few gigs of flash Linux would probably able to run on them. And things like this processor http://en.wikipedia.org/wiki/RAD750
would also run a standard realtime Linux without problems. Of course you wouldn't want to use a GUI on them, but I guess a combination of 2.4 Linux Kernel + busybox or GNU coreutils wouldn't be much less secure than the VxWorks used on the mars rovers and many more space based systems.
Don't forget unlike Windows there are already hundreds of mission critical systems running on Linux where an hour of downtime would possibly cost billions of dollars (the New York stock exchange servers are just a small example)
However I guess because of some idiot there are also Windows computers controlling mission critical stuff. (The worst thing i have seen so far were controlling computers at Houston (you can see them on the big monitors on Nasa TV though there is also a system running Red Hat), a windows 95 system controlling an artificial heart for a cell culture and coast guard safety systems)