The ref pts for the ASW patrol area can be made so the move with the group. Its fairly standard practice to do so. Look up relative reference points in the manual for an explanation.
To give just a little more help, look at the "Missions + Ref Points" menu. 3rd block down is "Make ref. point relative to" and your choices are fixed bearing or rotating bearing.
You select all the points you want (say, a box of 4), select the menu choice, then select the unit you want them to link to, probably in this case one of your frigates. Fixed means that they will always be oriented the same way no matter the course changes, maybe in a case you know the threat is from the east. Rotating is probably what you want, so that when the frigate changes course, the ASW box stays in front of the frigate, no matter what course it changes to. As thewood1 mentions, the explanations are in the manual on how to manage these. Works like a charm.
You can have multiple groups of ref points linked to a unit too. For example, a CVN task force, with a CAP box, or two or three, and one or more ASW boxes for helicopters out front and flanking, all of them rotating or fixed position to the task force. Very powerful and handy thing to get the hang of.
"When the Boogeyman goes to sleep he checks his closet for paratroopers"