If two work it suggests the problem is not with objFSO.CopyFile, but something else. Have you tried stepping through to see what happens?
BTW, you could simplify the code
strUserDatabasePath = "C:\ProgramData\Business Database"
strPath = "\\VirtualServer1\templates\Business Database\Graphics"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Icons"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database1.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database2.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database3.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database4.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database5.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath
strPath = "\\VirtualServer1\templates\Business Database\Database6.accdb"
If IfFileExist(strPath) Then objFSO.CopyFolder strPath, strUserDatabasePath