The task group won't respawn until the CV is sunk. When the CV is sunk, the whole TG respawns at its port 10 minutes later.
Actually what happens is when the CV goes down a timer starts...and ten minutes (10 Minutes) later the program destroys a map room bunker that is the master of the task group. The map room for the CV is hidden some where on the map, tucked away on some island or land mass near a corner of the map. Every CV also has a master field...typically a port, though not always. When the program destroys the CV map room, it checks CV master field, and if ownership has changed...the CV changes countries.
This system is used to prevent the direct capture of CV's.
When the CV re-spawns, it might be near its port...but its location is hardwired into the terrain and could be anywhere on the map as determined by the terrain designer. Many special events arena's have CV's without a port, and use an inland airfield or even a vehicle base as their master field.
It is possible on some SE maps to capture an inland airfield, destroy the CV and take ownership of it...as bizarre as that might sound.
Oneway