The test connect failures would be a result of an unstable link to ldap. I'd get your network folks onboard to check out the links between the app server. Also check the ldap server to see if it's having any issues of it's own.
As far as user logging in w/o problem when others fail, unless you've checked the "required" checkbox for the ldap auth, your default administrator account will still be usable. Also you can define omni admins who can log in regardless of the state of ldap (a good thing to be able to administer your system even in case of outage).
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