Embedded software running for long time
These bugs can be in the following cases:
1) The testing did not cover the full range of use cases, and the system encountered some untested input or sequence of inputs, engaging an untested logical path
2) The system has some time-dependent feature (something that is happening on a specific date or time, or after some specific long time.)
3) The system has some counters, which are stored in some wide variables, and then they overflow at some point causing some undefined behavior.
4) Hardware failure.

It is not easy to debug such a bugs after they happen, as it is hard to reproduce them. You can:

1) Log essential diagnostic data in order to examine it if something happens
2) Make the FW run in short cycles of time, resetting it every X  days/hours/weeks.