Seems a known issue: https://www.vmware.com/support/vsphere5/doc/vsphere-vcenter-server-51u1-release-notes.html#upgradeissues
Update of vCenter Server Appliance 5.1.x to vCenter Server Appliance 5.1 Update 1 halts at web UI while showing update status as installing updates*
When you attempt to upgrade vCenter Server Appliance 5.1.x to vCenter Server Appliance 5.1 Update 1, the update process halts for nearly an hour and the update status at Web UI shows as installing updates. However, eventually, the update completes successfully after an hour.
Workaround: None.