Prior to its Aug. 12, 2005 launch, NASA's Mars Reconnaissance Orbiter (MRO) was loaded up with 10 years worth of data projecting the future positions of Earth and the Sun. These locations are provided to the orbiter in the event of an unexpected computer shutdown.
That is, once the MRO's systems reboot, they first determine where they should position the craft's antenna for communication (Earth) and where it should position the solar arrays for power (Sun). To do this, they consult the aforementioned pre-loaded reference tables, which are set to expire next year. Needless to say, an orbiter without any way to correctly align its solar panels is a dead orbiter, and one without a way to contact Earth might as well be.
Note that the MRO has already experienced 16 unexpected shutdowns so far.
So, NASA is faced with the precarious task of rewriting the MRO's memory. This involves erasing and then rewriting everything. "It's the fundamental operating system of the spacecraft," MRO Project Manager Dan Johnston offered in a statement. "That's what adds risk. Just like with your home computer: If you mess with the operating system, the computer won't work."
The orbiter actually consists of two different, identical control systems. This is for redundancy's sake—one goes down and the craft can continue on. Each system comes with its own whopping 256 megabytes of flash memory, which has the helpful characteristic of being non-volatile, e.g. it doesn't get lost when the power goes down.
The systems will get their updates one at a time, with the first taking place next week and the next in early-2016. This has actually occurred already once, in 2009. Then, following a worrisome automatic reboot, engineers determined that the MRO's software was hiding a potentially devastating bug and would need to be fully replaced. Things went OK.
In any case, if the MRO was actually lost, we would have still gotten an extra seven "bonus" years of Martian science. The probe's planned lifespan was to be up in 2008. By now, it's hardly the only orbiter above the Red Planet and counts among its peers the Mars Odyssey and Mars Express orbiters (courtesy of NASA and the ESA, respectively), the MAVEN orbiter (NASA), and, as of 2014, the Mangalyaan orbiter (Indian Space Research Organization). Things are getting crowded, relatively speaking.