and your groups need to have high morale. if the fighters have been on CAP 100 during your approach to the battle area, they'll be tired out when you get to your strike-launch point. carrier air-groups are 'fragile', they can only run continuous ops for a limited time, then they need time off for rest/training to recover morale & reduce fatigue.
a carrier's groups need morale > 90 and fatigue < 10 when they enter the arena. running your fighters at 100 CAP might make you feel safe as you approach the battle area, but they'll be less effective when you get there. (well actually, they need lotsa other things, you've got to bring a sharp sword to the battle.)
if you need CAP during your approach, keep it at range=0 to minimize fatigue. w/ a multi-carrier group, micro-manage your CAP action every turn, trade off CAP duty among your available sqns, so that none of them gets over-used. don't go high-alt w/ your CAP fighters, that'll increase fatigue.
the thing is to bring your carrier air-groups to the battle, w/ their air-groups at peak power. you need high-trained air-groups (each w/ its own decent leader), then the carriers themselves must be well-supplied & have a decent TF commander.
high fatigue will screw you every time. imo, when fatigue > 20, it's time to retire. similarly, when air-group morale dips below 75, it's time to get out of Dodge. i mentioned that CAGs are fragile - the longer they stay in a fight, the longer it will take them to recover.