You can start by looking in the
log files; you should also post details about your hardware specification (specifically installed RAM); number of users, types of user (IMAP, POP, Web UI, etc.); how many users are online at the times these problems occur; whether this is a VM and if so, which hypervisor; I'd also suggest you check your DNS and hosts file configurations (see the 'Verify...' section of the
Split DNS article); is the /opt/zimbra directory on a RAID array and if, which RAID level; single server or multi-server install?