This seems to be related to the bug in ldap queries timing out in Zimbra 7 that I'd heard was fixed in Zimbra 8.something. We upgraded to 8.5 a couple days ago. In the admin interface today, I got:
Error code: CSFE_SVC_ERROR Method: SearchDirectoryRequest Details:HTTP response status 503
when doing an account lookup. And a user reported this error occurring after using the zimbra web interface for "a while":
A network service error has occurred.
msg: A network service error has occurred.
detail: HTTP response status 502
Any pointers would be appreciated, thanks!