As you can see on your posted table the calls were populated, but somehow the ADMIN_keepalive.pl process won't set the stats_flag='CLOSED'. They are all 'OPEN'. Further the row with daily 'TOTAL' seems to be missing (a reason for your symptom "No activity for...") . Possible reasons:
1. active_voicemail_server is not set to the right one
2. "Timeclock End Of Day" in system settings is not correct
3. time settings configuration issue
4. admin keepalive process doesn't start at certain times (or at all)
Post us from "/etc/astguiclient.conf" file the variables starting with "VARserver_ip" => and "VARactive_keepalives"
and from linux cli:
mysql -D asterisk -e 'SELECT `active_voicemail_server`,`timeclock_end_of_day`,`timeclock_last_reset_date` FROM `system_settings`;'
and crontab settings (from cli):
crontab -l