I'm sorry no one answered this! Annual poppies are monocarpic, so after they bloom and set seed they will die. In this way monocarpy allows them to make many more seeds all at once than perennial plants.
Depending on the type of annual poppy, you may not be able to make the plants live longer by cutting flowers. Some have very short bloom periods and want to die quickly after producing as many flowers/seeds as possible.
I grow various species of Papaver and Eschscholzia, and Eschscholzia seems to be more amenable to deadheading, but only by a bit. In some climates which are more arid than mine I imagine it would be more receptive.
