Most embedded system failures are due to power and I/O.
If you have robust power supplies from a reputable manufacturer (I like TDK/Lambda) with good filtering on the input (maybe external powerline filter modules), and you protect your external inputs and outputs, then the next thing to worry about is flash lifetime which should be measured in decades if you're not writing to it.
Problem with a Rasp Pi/Beaglebone is that it's running Linux and there are likely disk writes occurring, so your lifetime drops. If you can both limit disk writes and get long lifetime SSDs, I don't see why it shouldn't last at least 10 years.
If you have robust power supplies from a reputable manufacturer (I like TDK/Lambda) with good filtering on the input (maybe external powerline filter modules), and you protect your external inputs and outputs, then the next thing to worry about is flash lifetime which should be measured in decades if you're not writing to it.
Problem with a Rasp Pi/Beaglebone is that it's running Linux and there are likely disk writes occurring, so your lifetime drops. If you can both limit disk writes and get long lifetime SSDs, I don't see why it shouldn't last at least 10 years.