Rebuild index fail

Where are you seeing that error?
Do you have anything in the Event logs that indicate any other errors?

If the Error Code 57 is a win32 error message (which i think it might be) then it means
"A network adapter hardware error occurred"

So would make sure that the NIC Bindings of your network card are ok, and that the NET TCP Port Sharing service is started and that the Indexing Service itself is working, along with IIS

Is the Index Service local to the machine or is it on a dedicated server?
has it ever worked before?
Do other index queries like searches work ok?

Do you have a screenshot of the exact error?

That is really really odd that you'd get an access denied on your own server.
OK so for this user, the vault store they belong to , is it hosted by the same EV Server thats doing the indexing?