Whilst working on a Sitecore Commerce project last year I found myself stuck one day when I went to update profile definitions and found I could no longer access the Commerce Server Admin desktop tool. After a bit of debugging (and no error messages!) I found that my client had an Azure consultant in who made changes to how we would connect to the database server which ultimately changed all of our connection strings.
Like most Commerce Server connection strings, the MSCS Admin connection string is stored in the registry. Whilst the Commerce Server Admin desktop tool provides an interface for updating the connection strings for other sub system such as profiles and catalogs, it's not much help since it requires a connection to the MSCS Admin database. A quick search lead me to the blog post Manually setting CS2007 MSCS Admin database connection string which provides a console app for updating the encrypted values. Unfortunately the registry path values have changed since Commerce Server 2007 so it didn't work as-is. I've updated the app to work with Commerce Server 11 and you can find it on github here https://github.com/kjaneb/MSCSAdmin.ConnectionStrings.