IF it is in Moodle ...
Site Admin -> Security -> Site Policies
Account lockout threshold - default is no
Account lockout observation window - default is 30 Min
Account lockout duration - default is 30 Min.
Check permissions/ownerships on moodledata/sessions where session files are located for every login.
Check browser cookies one gets from the Moodle server - think there are two - one involves sesssion.
The error page, however, doesn't look to be the 'typical' Moodle
error page but an Operating system/Apache (Nginx/IIS) type error page.
Might check with hosting provider FAQ's client KB or helpdesk info as it could be a setting other than Moodle.
Search Google for "response 421 too many connections from this ip" and you'll see what I mean.
'spirit of sharing', Ken