This problem occurs because of a conflict between ntp.service and systemd-timesyncd.service. It's a known bug.
Why does this happen? It occurs on systems that have been upgraded to 19.10. ntp.service is carried over during an upgrade, and 19.10's systemd-timesyncd.server won't start in its presence.
more /lib/systemd/system/systemd-timesyncd.service.d/disable-with-time-daemon.conf
[Unit]
# don't run timesyncd if we have another NTP daemon installed
ConditionFileIsExecutable=!/usr/sbin/ntpd
ConditionFileIsExecutable=!/usr/sbin/openntpd
ConditionFileIsExecutable=!/usr/sbin/chronyd
ConditionFileIsExecutable=!/usr/sbin/VBoxService
See the following:
systemctl status ntp.service
● ntp.service - Network Time Service
Loaded: loaded (/lib/systemd/system/ntp.service; enabled; vendor preset: enab
Active: active (running) since Wed 2020-01-15 11:05:12 PST; 1h 21min ago
Docs: man:ntpd(8)
Main PID: 28740 (ntpd)
Tasks: 2 (limit: 4915)
Memory: 2.0M
CGroup: /system.slice/ntp.service
└─28740 /usr/sbin/ntpd -p /var/run/ntpd.pid -g -u 120:131
Jan 15 11:15:30 Satellite-E55 ntpd[28740]: 184.105.182.7 local addr 192.168.0.10
Jan 15 11:16:28 Satellite-E55 ntpd[28740]: 198.58.105.63 local addr 192.168.0.10
Jan 15 11:17:38 Satellite-E55 ntpd[28740]: 69.10.161.7 local addr 192.168.0.100
Jan 15 11:17:39 Satellite-E55 ntpd[28740]: 66.172.17.62 local addr 192.168.0.100
Jan 15 11:28:55 Satellite-E55 ntpd[28740]: 172.98.193.44 local addr 192.168.0.10
Jan 15 11:28:57 Satellite-E55 ntpd[28740]: 45.33.2.219 local addr 192.168.0.100
Jan 15 11:29:20 Satellite-E55 ntpd[28740]: 91.189.94.4 local addr 192.168.0.100
Jan 15 11:29:55 Satellite-E55 ntpd[28740]: 216.229.0.49 local addr 192.168.0.100
Jan 15 11:31:07 Satellite-E55 ntpd[28740]: 74.6.168.73 local addr 192.168.0.100
Jan 15 11:31:08 Satellite-E55 ntpd[28740]: 69.195.142.11 local addr 192.168.0.10
systemctl status systemd-timesyncd.service
● systemd-timesyncd.service - Network Time Synchronization
Loaded: loaded (/lib/systemd/system/systemd-timesyncd.service; disabled; vend
Drop-In: /lib/systemd/system/systemd-timesyncd.service.d
└─disable-with-time-daemon.conf
Active: inactive (dead)
Docs: man:systemd-timesyncd.service(8)
Jan 15 07:52:09 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:11 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:13 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:23 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:24 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:57 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:52:58 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:53:00 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:54:00 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
Jan 15 07:59:57 Satellite-E55 systemd[1]: Condition check resulted in Network Ti
One visual side effect of this problem can be seen in the Date & Time settings panel. You can't enable "Automatic Date & Time". The switch flips back to disabled.

However, ntp still does the time synchronization with the various ntp servers.
This can be fixed by uninstalling ntp, ntpdate, and sntp, and letting systemd-timesyncd.service perform the time synchronization.
Sources:
https://bugs.launchpad.net/ubuntu/+source/gnome-control-center/+bug/1858095
https://bugs.launchpad.net/ubuntu/+source/gnome-control-center/+bug/1848309
https://bugs.launchpad.net/ubuntu/+source/systemd/+bug/1849156