Trace unclosed connections
You can query sys.dm_exec_sessions on the last_request_end_time column to find open yet "sleeping" connections. 

From this, you can find out the last SQL executed

SELECT session_id, TEXT
FROM sys.dm_exec_connections c
CROSS APPLY sys.dm_exec_sql_text(c.most_recent_sql_handle) AS ST 
WHERE c.session_id = &lt;suspicious one from sys.dm_exec_sessions&gt;