I hope it isn't too late, but maybe its the soil? My poppies did terrible in my front yard with bad soil, and in the fertile soil out back, the did just wonderful, they are still blooming even right now .
The Poppy's you have are bread for gardens and therefore require a nice rich soil with added compost / manure added to the planting area and hole you intend to place the plants into, this type of soil helps feed the long roots these plants grow and also helps keep air and moisture into the root area. Poppie's are greedy plants, and when grown on very poor soil the do develope the symptoms you are discribing but hey, there is always the exception to the rule and am sure other can come in and say, "well my poppies grow anywhere, mine do because after several years of the plants maturing, they have self seeded into the grave paths and after a couple of month there I have to lift them as they deteriorate quite quickly,
Maybe you still have time to carefully lift your plants up and add some compost / other matter that will improve the soil or even move the plants to another spot all together. Poppies are plants that expand in size each year and after several years you end up with nice large clumps with many flowering stems, sadly the flowers only last about a day or 2 but IF you deadhead them regularly the keep sending out more flowering stems,
IF you want to increase your plants after a few years do this by root cuttings (scrape away some earth around the roots, pick a nice root about as thick as a pencil, cut this out and place it into compost watered and kept in a cool area till you see shoots growing and repot till large enough to go out in the border) OR grow from seed. (when the poppy seed heads start to turn brown and are looking like they are dried out, remove the seed head, slace this in a paper bag and gently shake all the MINUTE seeds out, there will be hundreds, when you sow the seeds, I dont cover them till I see little green tips and even then I'd rather not cover them, after 2 sets of leaves come, repot the little plants individually till they can be grown outside.
Hope all this helps you understand your plants and also how to care for them.
Good luck hope it's not toooooo late for you.