SQL Server 2012, triggers missing after restore database
A wild guess - are the triggers based on CLR code? If CLR Integration has not been enabled on the machine you are restoring to then the triggers won't work.

CLR Integration can be enabled with the following code.

exec sp_configure 'show advanced options', 1;
GO
RECONFIGURE;
GO
exec sp_configure 'clr enabled', 1;
GO
RECONFIGURE;
GO