Well would be easier if you had the logs from the vCenter server itself 
You can have a look at the /var/log/vpxa.log on the ESXi side and look for timeouts and backtraces as this is the service on the host side communicating with vCenter Server. This most likely will only give you a timestamp and an indication that vCenter Server was shutdown or not reachable. What it will not tell is the reason why.
You will find this information only in the vCenter Server logs, namely the vpxd.log if you search for "Shutdown" or "Backtrace".