When you repair the broken sources and save the map document, are you repairing those data sources with an older SDE connection file? Should be brand new 10.1 connection files ... we actually did a repair as well as a uninstall/reinstall of the software on the machine in question.
To keep things clean, I would suggest creating a new SDE connection file from ArcGIS Desktop 10.1 and then re-pathing all of the broken sources with that brand new connection file. I could try this again ... in case I perhaps neglected to actually perform this task.
You might also want to perform a Save As for your map documents from ArcGIS Desktop 10.1 just in case you might still be using a 9.x map document without even knowing it. We tried this a few times ... if anything, they would save to a 10.0 document as that's what we migrated from in early fall of last year. In fact, we haven't had 9.3.1 on any of the organization's machines since the summer of 2010.
This actually worked out as would have had to perform this operation twice due to the changes that were made to SDE connections between v10.0 and v10.1-10.2.