It's just a possibility, though I would think you'd be getting a connection error if that were the case. Which RDBMS platform (Oracle 11g, SQL Server 2012, etc.)? If you have access to the RDBMS tools such as SQL Server Studio Manager or SQL Developer, then one simple thing to try is to check and see if the account you're using is still connected to the database when the issue in ArcMap occurs again. In other words, when the selection problem happens again, leave ArcMap open and check to see if your session still exists in the database.