Hi,
I think you might be seeing the connection timeouts which is default of 1 Hour for TCP.
UDP is 2 Mins.
Try increasing the timout on the ASA device and see if that works for you:-
http://www.cisco.com/c/en/us/td/docs/security/asa/asa82/configuration/guide/config/conns_connlimits.html
Thanks and Regards,
Vibhor Amrodia