The EHI is essentially an SMI-S provider.   It has it's own user/password, independent of the host itself.   Are you using the EHI user/password?  Or ActiveDirectory/Windows credentials?  Make sure that the Windows firewall is either disabled, or allows 5988/5989 inbound.
I'm trying to discover a Windows Physical hosts in SRM through Host Agent (EHI). I did install the host interface in target windows host. When trying to discover in Centralized management, it fails. The Test result shows "Testing CIM API authentication" failed. Please provide your suggestions. The target host is windows 2008 R2.
Discovering Windows 2008 R2 Physical host