They will stop hnting after 30mins of no contact, if they re-establish contact with you the counter will start again.
It has been known for DD's to actually loose contact with the convoy that they were protecting.
You can change this time limit & infact previous versions of SH3Cmdr (IIRC) had a time limit of 45mins. I just can't remember the correct file at the moment.
EDIT - Found it, in the Sim.cfg file the is an entry called AI detection and the default for GWX is 23mins. I think this is set to this time to stop the issue about escorts loosing contact with the convoy. So change this at your peril.
