Experts and BHG readers answer.
Well there are many different species of poppies (Iceland, Oriental, Shirley, etc) so it would help to know what kind of poppies you have. Also, some of the ones I listed above have a tendency to have drooping flower heads. I can't tell from your question if the flower heads are the problem or the whole stalk. Poppies also need a lot of sun, but again, without more information I can't guess what's going on. If you want, repost the question with more details (type of poppy, where planted, light, etc).