Maybe a lite bit late, but I manage to make work Veeam 7 under an ESXi 5.5 environment (3 servers under Vcenter administration with essential kit licence).
The key is enabling SSLv3 in every ESXi host.
I use this tech note:https://kb.vmware.com/selfservice/micro ... hostd5.53e
Under my 2 ESXi 5.5 Update3 hosts (the third one is 5.1)
I only enable SSLv3 for this service: Authd - Port 902
I hope this help someone.
I surf the web the last 2 days looking for an answer.