Returning to the topic of discussion, I have the same problem using Gnome Classic which should be very stable, and It's almost always while logged on. The mouse is lost, and the keyboard is lost and won't respond to [Ctrl]-[Alt]-[Back Space], and I'm forced to warm reboot, which can't be good for any file system. It's not the power supply, because it still happens after extra drives are disconnected. I've written a few Windows screen savers, and eventually I was able to get them to look and run the same under Win95, 98, XP, and Windows 7. The one most important thing I learned was any attempt to cheat on the proper handling of GDI and it's functions resulted in system hangs, and or bad output, that eventually led to system hangs or stoppages after so many iteration loops, since a screen saver is a timer loop.
So the suspects are Mozilla Firefox, Gnome Classic, the window manager and the X11 subsystem that the window manager uses. Since this is a multi Session issue, say Gnome Classic and Cinnamon, without knowing a lot about programming in a Linux environment, or X11 or the window manager in use, which are all output devices from a code point of view, I would say the problem is the desktop output or Firefox to wither the window manager, or that X11 subsystem.
It's not a hardware problem, what's causing the desktop freeze is a software memory management issue, which could be solved by a well documented and standardized software interface between the desktop, their applications and the what ever subsystem is dealing with user input and graphical output.
One method of further investigation would be to log into another desktop, that uses a different window manager, maybe Xfce, and see if that hangs, if it doesn't then it points to the window manager. Keep in mind I'm new at this stuff.