Find when a specific database went offline and the reason for same
At minimum, please check sql logs, for example, if I purposely take a db offline using

alter database [TestDB] set offline with rollback immediate;


I can see in SQL Server log, the following message


  Date      10/24/2016 12:28:57 PM Log      SQL Server (Current - 10/24/2016
  12:00:00 AM)
  
  Source        spid51
  
  Message Setting database option OFFLINE to ON for database 'TestDB'.