In the 1977 movie, Star Wars Episode IV, orders to excecute the princess are given several times. Once an order to execute her "immediately" but still she was not executed and was later rescued. Why was she not executed?
I think Lucas was employing a plot trope called, Always Save the Girl. The effect of having a wait associated with the character moves the plot along.
There are also other ways to look at it: aside from the dramatic effect of waiting, there may have been bureaucratic obstacles (the Empire is a government entity after all). And the timeline of events issue raised by a previous poster. Additionally, Darth Vader is powerful in the ways of the Force and could possibly foreseen future events regarding the escape of Leia and the discovery of his son.
Also, the movie and the story were written in an earlier time when people were more innocent than we are today. Look at American Graffiti; another great movie by George Lucas.