You could try deleting the renaming the essbase.sec and trying to start the essbase service again, hopefully it should register again with Shared Services.
It has worked.
Thanks for your help.
Obviously several months later now, but just want to say thank you as well - I was having the exact same issue as the original poster (Essbase Server missing from Shared Services, credential error from EAS, etc). Your solution worked perfectly for me as well. That you for this solution.