Fail2Ban stops by itself.
Fail2Ban can be enabled successfully through Tools & Settings > Services Management.
Fail2Ban is enabled (The option Enable Intrusion Detection is checked at Tools & Settings > IP Address Banning (Fail2Ban) > Settings)
No jails are active in Fail2Ban.
Enable Fail2Ban jails:
In Plesk go to Tools & Settings > IP Address Banning (Fail2Ban) > Settings.
Check the option Enable intrusion detection and apply the changes.
Switch to the Jails tab and activate at least one jail.