TJ Cloutier and Tom McEvoy point out that in some cases the best strategy with a short stack is to put in a small raise before the flop then go for it post-flop.
This strategy works against blinds that might not call an all-in bet when you have a hand but will call a small raise. Even if they fold after the flop you've picked up more chips.
It also works against some blinds that will call an all-in bet (since they want to "protect" their blinds) but will not call an all-in bet post-flop if the flop doesn't help them.
Of course if I have to put in half or more of my chips just to call or make a small raise I'll just stick them all in there.
The play that you are referring to is called a stop-n-go (call or min-raise preflop then push on the flop if you think your opponent missed)
Calling with half of your stack is a MISTAKE...I see players all the time do this, miss the flop, then fold to a bet... If you are under 5BB you really need to push and hope you double up, you are simply losing chips if you limp hands.