Jed, I wondered about that exact question when I printed the Bahn answer. Having never used a Dauer-Spezial ticket, let alone missed a Dauer-Spezial connection, I can't answer that. I can, however, say, from experience, based on almost 200 connections in 8 years, that only once have I missed a connection because of a train being late, and that was by a mile (½ hour, actually). I was on a train from Stuttgart to Ulm on a Friday afternoon, and the train was late into Stuttgart and consequently late into Ulm. As we approached Ulm, the conductor came on the PA system and started reading off a list of connecting trains that were being held and their track. (When he got to my train, he said that it, "unfortunately could not wait". But the following train was only a half hour behind it.)
My point is that DB is very aware of connecting trains and makes every effort to make sure you make the connection, holding the connecting train a few minutes, if necessary. If you have a close connection, and your train is late, you should notify your conductor. It's kind of like on an air connection.