We observed that if one/more of the data source is down (if database is down or expired password), when we restart the managed server it doesn't start and remains in Admin state. The reason behind that is the Initial and Minimum capacity specified in Data Source. E.g. for majority of the cases, when we create data-source, following values are set to 1 by default, which was causing problem.
Changing them to 0, resolves the restart issue. There are still tons of constant error in logs related to the data source which is down, but at least server comes up fine.