Вот похожая ошибка в комментариях:

https://serveradmin.ru/ustanovka-i-nastroyka-zabbix-3-4-na-centos-7/#comment-2778

Это вы или другой человек?

Другой. И ошибка в логе другая.

10947:20171102:115807.471 Starting Zabbix Server. Zabbix 3.4.3 (revision 73588).
 10947:20171102:115807.471 *** Enabled features 
 10947:20171102:115807.471 SNMP monitoring: YES
 10947:20171102:115807.471 IPMI monitoring: YES
 10947:20171102:115807.471 Web monitoring: YES
 10947:20171102:115807.471 VMware monitoring: YES
 10947:20171102:115807.471 SMTP authentication: YES
 10947:20171102:115807.471 Jabber notifications: YES
 10947:20171102:115807.471 Ez Texting notifications: YES
 10947:20171102:115807.471 ODBC: YES
 10947:20171102:115807.471 SSH2 support: YES
 10947:20171102:115807.471 IPv6 support: YES
 10947:20171102:115807.471 TLS support: YES
 10947:20171102:115807.472 ***************************
 10947:20171102:115807.472 using configuration file: /etc/zabbix/zabbix_server.conf
 10947:20171102:115807.482 current database version (mandatory/optional): 03040000/03040005
 10947:20171102:115807.482 required mandatory version: 03040000
 10947:20171102:115807.501 server #0 started [main process]
 10952:20171102:115807.502 server #1 started [configuration syncer #1]
 10953:20171102:115807.503 server #2 started [alerter #1]
 10954:20171102:115807.503 server #3 started [alerter #2]
 10955:20171102:115807.504 server #4 started [alerter #3]
 10956:20171102:115807.505 server #5 started [housekeeper #1]
 10957:20171102:115807.505 server #6 started [timer #1]
 10959:20171102:115807.506 server #7 started [http poller #1]
 10963:20171102:115807.509 server #10 started [history syncer #2]
 10964:20171102:115807.509 server #11 started [history syncer #3]
 10967:20171102:115807.511 server #12 started [history syncer #4]
 10968:20171102:115807.512 server #13 started [escalator #1]
 10970:20171102:115807.517 server #14 started [proxy poller #1]
 10960:20171102:115807.517 server #8 started [discoverer #1]
 10971:20171102:115807.522 server #15 started [self-monitoring #1]
 10974:20171102:115807.523 server #18 started [poller #2]
 10962:20171102:115807.528 server #9 started [history syncer #1]
 10976:20171102:115807.533 server #19 started [poller #3]
 10972:20171102:115807.539 server #16 started [task manager #1]
 10973:20171102:115807.540 server #17 started [poller #1]
 10981:20171102:115807.546 server #23 started [trapper #1]
 10978:20171102:115807.550 server #20 started [poller #4]
 10984:20171102:115807.551 server #25 started [trapper #3]
 10985:20171102:115807.556 server #26 started [trapper #4]
 10986:20171102:115807.561 server #27 started [trapper #5]
 10979:20171102:115807.572 server #21 started [poller #5]
 10980:20171102:115807.585 server #22 started [unreachable poller #1]
 10989:20171102:115807.587 server #30 started [preprocessing manager #1]
 10982:20171102:115807.595 server #24 started [trapper #2]
 10987:20171102:115807.600 server #28 started [icmp pinger #1]
 10988:20171102:115807.600 server #29 started [alert manager #1]
 10996:20171102:115807.611 server #32 started [preprocessing worker #2]
 10997:20171102:115807.624 server #33 started [preprocessing worker #3]
 10990:20171102:115807.656 server #31 started [preprocessing worker #1]
 10947:20171102:120234.081 Got signal [signal:15(SIGTERM),sender_pid:11109,sender_uid:0,reason:0]. Exiting ...
 10947:20171102:120236.083 [Z3001] connection to database 'zabbix' failed: [2002] Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)

Причём с прошлой версией на ubuntu такая же проблема была. Сначала всё работает хорошо, как только массово добавляю хосты всё падает, но ошибка там другая была.

Тут то четко в логе написано, что отваливается соединение с mysql. Надо в эту сторону смотреть. 

Вот еще похожее падение - https://serveradmin.ru/monitoring-asterisk-v-zabbix/#comment-2793  Только без информации о проблемах с подключением к базе.