In the ADMS Console, clicking Tools>Administration I was getting the message in the title.
Similarly, RMB on the Vault under "File Stores" then select "Replicated Folders" resulted in the same message. ("Object reference not set to an instance of an object")
Also, filestore replication was not working, the number of unreplicated files was never reducing. (no errors in the vault logs)
ADMS Console backups were not running at all. They were starting, but never finishing and no error messages.
In the end, after much investigation, the solution was a little obscure. In IIS, someone had edited the Bindings in the Default Web Site. The "Host Name" is normally blank, meaning that calls to "localhost" and the loopback address get resolved correctly. They had replaced a blank with the Computername, meaning that hard-coded calls to "localhost" were not being resolved correctly. After removing this, and restarting the machine, all the above symptoms disappeared.