Grant User Permission To Restore Database And Access that database in sql server?
But when I restore another database backup that gets disconnected, i.e. not accessible.


You have to add the user to the db_owner role after the restore. You can use 

ALTER ROLE [db_owner] ADD MEMBER [frank]


or EXEC sp_addrolemember 'db_owner', 'frank';

Note:

ALTER ANY DATABASE - You dont want to give the user too much rights since this will allow the user rights for all the databases.


  Grants or denies the ability to drop or modify existing databases as well as create new databases. The dbcreator fixed server role has this permission granted implicitly.