Accounts inexplicably removed from "Accounts & sync"
After some months of additional observation, I'm pretty certain that the accounts disappear when the free internal space gets low, usually when I'm down to 12 MB or so. Presumably, Android tries to free up some internal space occupied by app data, and the accounts seem to be the first to go. 

Due to the low internal storage, I have moved all apps to the external storage, so this might as well be a factor, as Izzy mentions in the comments.