I regularly use data from different sources (SDE connections, network drives, over a VPN, etc).  In the past, I often found that if I closed out of ArcMap, the next time I opened it and tried to add data it would have to spend time trying to re-connect to a folder that was no longer accessible.  Sometimes this could take ages.

I used to get around this by trying to remember to add some local data to ArcMap before I closed it (not a very reliable work-around, as more often than not I would forget to do this).

The more reliable solution is a quick Options setting in ArcMap.  Under Tools > Options > General Tab, uncheck "Return to last used location when Add Data dialog first used".