Strored procedures start timeouting all of a sudden in MS Sql Server

Stored procedures suddenly start timeouting when called from a .NET application, seemingly without any particular reason and without warning.

System.ComponentModel.Win32Exception (0x80004005): The wait operation timed out

It is never the same stored procedure to time out first, but when the first stored procedure gets timed out all following calls to any procedure in the database are timed out.

I have optimised all the heavy procedures, checked and optimised indexes, made sure there are no transactions active to lock the resourecs... but somehow this keeps happening. Some times it happens after a few day, some times only after a few hours, and there seems to be no consisten pattern in timig.

The funny thing is that the problem started only last month. The database is live for about 5 years now, and the latest modifications were made in february.

Does anyone have any idea what could go wrong?