What prevents a commercial jet from electronically "resetting" the way a computer sometimes does?
I'm a programmer and private pilot, so maybe I can help dispel some of those fears.


The computers that run a commercial airplane are conceptually much simpler than the one that runs your phone. This means far less chance of a bug in the software, just because there's less for the programmer to keep track of.
If your phone restarts, it doesn't imperil anybody's life. So, the testing and Q.A. for such a device is basically whatever the company wants to do. On the other hand, computers in aviation are much more thoroughly tested before they can be certified to fly.
Similarly to point 1, the computers on an airplane each have only one job. A lot of the crashes on a typical PC or smartphone come from different apps stepping on each other's toes. (The operating system is supposed to keep each app apart so they can't do that, but point 2 applies to operating systems as well.)
The airplane isn't one single computer, like your phone. Yes, your phone probably has multiple processors, each with multiple cores, but they're tightly coupled together in order to form one computer. The computers on an airplane are networked together, but they are separate computers. If your phone crashes, even if the guy sitting next to you is on the same network, it doesn't affect him, does it? Similarly, if the FADEC for one engine fails (a vanishingly rare occurrence, because FADECs are conceptually among the simplest of computers), all that will happen is that one engine will shut down, with no effect on the rest of the plane.
On the other hand, the really important computers (such as fly-by-wire controllers) have multiple redundancies. So, if one fails, the rest of them can pick up the slack. Even the pilot wouldn't notice except for the warning light that would show in the cockpit.


If you want to see what actually happens when things fail on an airplane, take a look at the following videos:


Complete avionics failure over the ocean.



   The pilot flew the airplane by hand while he shut down and restarted the avionics. The flight then proceeded normally.



Autopilot failure. (Ironically, the same guy as the previous link!)



   The pilot actually let the autopilot have it for a few seconds, just out of curiosity as to where it would take them. But once it started banking more than it was supposed to, he disengaged the autopilot and took over manual control with no issue.



Brand new pilot (less than 60 hours total flying time) suffers complete electrical failure at night



   Engine stayed running despite losing all electrical power to the entire plane. He landed safely.


Edit: Well, just two hours ago as I type this, another video of an in-flight failure just happened to pop up in my YouTube feed:


Generator failure in flight



   He switched to his backup generator, and other than an annoying whine in the headphones, had no other issue with the flight.