I have a 2 monitor setup (Intel IGPU), running Kubuntu 16.10. Several times a day (I think it's when the monitors go in or out of power savings mode), the panel disappears; sometimes it re-appears in the same place, sometimes it re-appears on the other monitor (so over the course of a day it might move back and forth between the two monitors), and sometimes it doesn't re-appear at all. I figured out that when it disappears completely, I can edit ~/.config/plasma-org.kde.plasma.desktop-appletsrc, search for all instances of 'lastScreen=X' and replace X with 0 or 1, and restart plasmashell. Interestingly, and this is probably the source of the bug, when I look at all the values of X in the file, it's full of invalid screen numbers - just now I saw values range between 0 and 8. For some reason it seems to be incrementing the screen number at some point, even though it gets to invalid values, rather than limiting them to only valid screen numbers. And to clarify, there is no reason for it to be updating this value at all as far as I know... I'm not actually moving the panel or other widgets around between screens.
This should be fixed with Plasma 5.8.4. Please add a comment when you update to that version.
multiscreen management different in 5.8, if something similar happens, is a different bug
When 5.8.4 or later is backported to Kubuntu 16.10, I'll install and test it. They used to backport every point release, but nowadays it seems there are large gaps in KDE backports.
I think it is indeed solved in 5.8.4. Although the panel does sometimes move from one monitor to the other after returning from monitor power savings mode, it no longer disappears completely nor moves to an invalid monitor number.