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.
I have successfully taken rose cuttings with both new and old wood. It is important to let the new stems sufficiently mature. The new wood is usually mature enough after the stem has just finished blooming. If you don't let the stem mature enough, then it usually becomes limp and will die before you can get it to root. I take cuttings from new rose stems in the spring right after the first bloom cycle. Then in early to late fall (in Southern California) I prefer to use more mature or old wood. When using old wood in the fall, I will remove the rose cuttings from the Mason jar, baggie, or mister, after only several weeks since it is cool enough then for them to root on their own as long as I water them daily.
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.
When you transplant your roses, be sure to dig a much bigger hole than you think you need (for most types, the planting hole should be about 15 to 18 inches wide), and add plenty of organic matter such as compost or aged manure. This will feed your plant in the years ahead. Some old-timers recommend placing a 4-inch square of gypsum wallboard and a 16-penny nail in the hole to provide calcium and iron, both appreciated by roses.
Plant the rose cuttings at any point throughout the year. Some people like to plant them during the cool months, while others wait until the early summer. Rose cuttings should be able to grow during any season. However, keep in mind that they'll need to be constantly watered, so if you plant them during the summer or live in a hot climate, they're going to dry out faster. For this reason, the rainy season might be your best option.
There will be disappointments along the way, when many rose seeds fail to germinate, or perhaps they do germinate, only to die several weeks later from damp-off disease. Sometimes a rose seedling will turn out to be as ugly as sin, or very sickly, and you will reluctantly have to throw it away. Other times they will be just ho-hum, or look too much like its parent, and therefore have no value. But, just when you don't expect it, you might discover that one of your rose seedlings turns out to be very special.