I too, have tried the cut rose flower method, but haven't yet been successful--perhaps because there are chemical additives that the roses have soaked up, or because there are no nodes (which are the points where new shoots grow out), or because the stems have spent much of their energy producing the flowers...BUT, perhaps if the flowers were immediately cut off and some rooting hormones applied to the bottom cut ends, that may work.
Remove the seeds from the fridge. Try to do this around the time that the seeds would normally start to germinate, such as in early spring. Make sure that the environment outside of the fridge is about 70 degrees Fahrenheit.[3] The seed will not sprout until you take them out of the fridge. Depending on the rose variety and individual seeds, the seeds could take anywhere from four to sixteen weeks to germinate. Often, 70% or more of the seeds never sprout at all.[4]

Some people don't bother to take the time to do this, but others do. While the rose seeds are soaking, you will see that some sink to the bottom and some float on the top. The seeds that float are sometimes not viable, so you might want to throw them away. The rose seeds that sink are said to be the good ones, and are the ones to plant. There are pros and cons to this theory, and many rose hybridizers simply plant all the rose seeds that are harvested.   

Plant the seeds. Some store-bought seeds can be planted immediately. If you germinated your own seeds as described above, plant them as soon as they begin to sprout. Plant with the sprout pointed downward, as this is the root. Lightly cover them with soil, about 1/4 inch (6 mm) deep. Space seeds at least 2 inches (5 cm) apart to minimize competition.[5]
Fertilize the roses. After they are established, roses should be fertilized a few times per growing season. Use fertilizer (either liquid or granule) in early spring, when you see the first few leaves sprout. Use it again after the first bloom, and again if there's another bloom. Stop fertilizing the roses at the end of the summer, just before Labor Day.[7]
Remove the rose hips once ripe. The rose hips will start out small and green, then change color as they grow until they are completely red, orange, brown, or purple. You may pick them at this point, or wait until they are just beginning to dry out and wrinkle. Don't wait until they are fully dry and brown, as the seeds inside may have died by this point.
Be aware of your variety’s needs. Rose care will depend a lot on the variety you’re raising. Some roses like William Baffin and Lady Hillingdon climbing roses are more drought tolerant, for example, while others need more water. Some varieties can withstand less sunlight than others. Rose varieties should also be pruned differently depending on the variety and your climate area.

If you order bare-root roses from a mail-order company, order early (late winter or early spring). The roses are usually shipped in the spring because bare roots when plants are fully dormant, well before they have leafed out. They’ll look like a bundle of sticks on arrival. Note that they are not dead—simply dormant. Check that the packing material is moist and keep them in a cool dark place until ready to plant.

Numerous things could be influencing the plant, from soil quality (do you amend and or feed/fertilize it?) to the circumstances of the move. It’s best to transplant roses in spring or ofall, not midsummer. and the new location should have plenty of organic matter/aged manure (these are amendments, per above). And then there’s watering … . So we really can not tell from here.
Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.