You always need extra fuel!
And that is the major weakness of an aircraft carrier. It needs lots and lots of aviation fuel because whatever its storage capacity might be, in intensive flying operations, it needs topping up very frequently. And if it's non-nuclear engined, it needs a lot of fuel just to keep steaming round. A cunning enemy wouldn't both trying to penetrate a carrier air group's defences - simply disrupting the (very) vulnerable flow of supply ships would bring things to a grinding halt very quickly.