Can you check if the following errors appear in /opt/APC/PowerChute/group1/error.log:
ERROR Thread-35 com.apcc.m11.components.Shutdowner.ShutdownSequencer - performShutdownForESXiStandaloneConfiguration
com.vmware.vim25.RestrictedVersion
ERROR pool-2-thread-1 com.apcc.m11.components.Shutdowner.CheckIfCriticalEventActive - processCriticalEventExceptClusterMode
com.vmware.vim25.RestrictedVersion
This error - "com.vmware.vim25.RestrictedVersion" usually points to a licensing issue e.g. attempting to shutdown the Free/Unlicensed version of ESXi.
https://www.vmware.com/support/developer/vc-sdk/visdk41pubs/ApiReference/vim.fault.RestrictedVersion...
http://sourceforge.net/p/vijava/discussion/823526/thread/0224ed4c
http://sourceforge.net/p/vijava/discussion/826592/thread/3ee70cd7
http://www.virtuallyghetto.com/2011/06/dreaded-faultrestrictedversionsummary.html
Can you confirm if it is the free version of ESXi 5.5 or a licensed version? If licensed, can you specify the license type?
PowerChute Network Shutdown does not support the free version of ESXi. The following Kbase provides details on how to perform ESXi host shutdown for the free version:
shutdownHostViaSOAPAPICall.pl for ESX(i) licensed and free version