It's not really a "gut feeling" thing at all. Here's the two hands people have made up as possible continuation bets.
1)
[ QUOTE ]
5-Handed 50/100
Hero(1300): AK raise to 300
CO (2000): Calls
Folds
Flop 378 rainbow
pot is 750
Hero goes allin 1000
[/ QUOTE ]
2)[ QUOTE ]
5-Handed 50/100
Hero (1300): AK raise to 300 CO+1
folds
SB (2000): call
Flop: Q49 rainbow
pot is t700
SB Checks
Hero bets 375
[/ QUOTE ]
The reasons to continuation-bet in hand 2 and not in hand 1 include...
<ul type="square">[*]You are in position and your opponent has shown weakness by checking.[*]The Q on the board can scare hands like any non-premium pocket pair that hasn't hit a set and Ax/Kx hands that have one overcard to the board instead of two.[*] Your opponent's call from a blind usually indicates a weaker hand than a call from a non-blind position.[*] In the event your c-bet gets called, you will likely see two more cards instead of just one, since most opponents will check the turn OOP even if they think their hand is best.[/list]
The fact is you have a lot more folding equity in hand 2 than hand 1, and your hand has more potential showdown value the times you do get called. It's just basic SNG math rather than poker gut instinct.