I installed Ubuntu 20.04 with Xfce4 DE (xubuntu-desktop) on a Raspberry Pi 4 4GB.
System runs good but randomly it shutdowns/halts, I don't known exactly what happens because I use it as headless server and connect via SSH or VNC. When I can't connect to it, I go where the Pi is and I find it with both leds (activity and power) off. There is a little fan connected to +3.3 V pin of GPIO for cooling and it is on...
I'm sure there aren't hardware failure because the Pi runs like a charm with Raspbian Buster OS!
I have put some more time into this problem. After running stable for 24h hours now I am quite certain the issue is related to the suspend feature offered by the hardware and several desktop environments. The Raspberry Pi either fails to wake from suspend or fails to suspend.
What solved the issue for me was turning off Auto-suspend. For example, Gnome allows you to set suspend under System Settings -> Power. The Auto-suspend setting there is enabled by default. If you change that setting to Never, the Raspberry will run stable.
On a somewhat related note, it would be very nice to have kdump/kexec work on the Pi. Did someone ever figure out an initramfs/cmdline that works?
I replaced Gnome with XFCE and it works without crashing. I made this decision because with the remote access via ssh it still worked, unfortunately a BUG in Gnome causes this to crash, even disabling the items with reference to power did not solve the problem.
I have similar experience - I wanted to install kubuntu desktop and it says it is installed, but there is no way of login into it - just option for the Ubuntu. The same with lubuntu. So i ended with installing the full Ubuntu desktop, which is not somewhat OK, but if I log out, the system crashes with just cursor on the screen; hard reset required. Also it would crash after the system goes to sleep/hybernation. Pretty annoying - Raspbian is running perfect. Also, from the beginning I am having problem with only one, quite low and weird resolution available for my 4k Samsung display. Sadly, there is nothing yet to be found on internet suggesting, what kind of problem it could be and how to fix it...
I have found that the Gnome desktop is causing the problem. Killing all gnome processes on the Raspi gave me a stable machine. It now runs for 18 hours without a problem. Before it would halt every 30 mins or so... I am running the machine headless.
Still a little early, but with suspend turned off my Rasp Pi with lubuntu desktop is running longer than it ever has without locking up.
Go to Settings → Session and Startup and disable: