Take a look at the Field Summary section of
http://www.hibernate.org/hib_docs/v3/api/org/hibernate/ConnectionReleaseMode.html
In Hibernate 3.1 or later, by default JDBC connections are automatically released at the end of a transaction (it's using the AFTER_TRANSACTION option from the link above) and reconncected as necessary. So the only reason you would ever need to explicitly reconnect in the session is if you're using application-supplied connections (i.e. you're *not* using a connection pool). And in that case you have to provide the Connection object using reconnect(Connection), so the no-argument reconnect() is unnecessary.
This is good news. It means you don't have to store any connections in your session or do anything special with the connections. The default in Hibernate 3.1 or later is to aggressively release the connection at the end of a transaction and reconnect for you automatically as necessary.