If you get the User id and time frame from the logs you may be able to go to the Transaction Manager or ask them what they were doing at that time to get a clue and narrow things down. I would also look for other clues like confirmations or goods movements in SAP or whatever business systems you are using etc. You can try turning up logging to info for the com.sap.xmii.Illuminator.templates.DBQuery location or similar but depending on when your exception is thrown it may not get there. I would be very careful turning up logging, especially if you have stressed system. Posting the full exception message might help too.
Regards,
Christian