Sometimes it takes that long for them to be mature enough to sustain a bloom. Alternately they might be planted a bit too deep (shouldn't be more than 2" below the surface) or they might have botrytis, a disease that can impact the flower bud. Usually you'll see signs of it on the leaves and stems as well, with them appearing unhealthy and wilty.

It can be frustrating because you say - "Maybe next year... " and the next year comes and it's disappointment. Another thought is that the original plant had a bare minimum of eyes and has been spending all this time forming more. Hopefully it's a simple problem.

What you describe is often called bud blast. It can be caused by environmental conditions at a critical stage of development such as frost or drought. It can also be caused by a fungal attack, usually during cold wet periods. In these cases the problem is unlikely to be repeated the following year and the plant will likely continue to thrive.

If the problem happens next year you might also suspect a nutritional problem, likely not enough potassium, too much shade or that the plant is planted too deeply. All of these are correctable by either adding fertilizer or moving the plant to a more suitable location in the case of shade or planting to deeply.

Bud blast often occurs in newly planted peonies. Peonies form their buds in the fall. If a plant is divided and replanted in the fall (as it should be) the previously formed buds will continue their growth in the spring on a much-reduced root system. Often the newly divided plant does not have the "strength" to fully develop all the buds and they just dry up. As the plant matures this problem disappears.

Here is your solution for the problem:
1. Get the roses relocated way from the Peonies or at least feed the roses with a balanced rose food so that they do not suck the nutruients from the peonies.
2. Cut back other vegatation to allow at least 6 hours of good full sun on the peonies. Shade only weakens them, also the uv light will kill fungis that might be effecting them.
3. Dig a circle around the peonies working in tword the roots. when you come to the roots, dig under them a little ways. Now fill this up with WELL DECAYED compost with a 5-10-5 or a 10-10-10 fertilizer mixture. About 1 to 2 cups of fertilizer. Bone meal may also be used, as it is 5-10-5 equivelent. NEVER< NEVER4. Scrape away the soil at the crown and check the depth. It should be 1 to 2 inches. If it is too deep the peony will not bloom at all, Bud Blast ocurrs to the blooms and eyes, therefore I dought the peony is too deep or it would not produce buds or blooms, but check it anyway and correct the depth if needed.
5. Water the peony several times in the winter. DO NOT water the crown, but rather water around the crown staying at least 6 inches away and allowing the water to soak downward to the roots. Watering the crown causes fungis and crown rot.
6. Refertilise after blooming and in the fall with 5-10-10 or 5-10-5 and bone beal working it in from the top of the soil every year, and add compost to the ring every year in the fall with the fertiliser.

THE RESULT:
On a new 1 to 3 eye division the roots will grow about six inches the first year, and an additiona 12 the secound year. At the end of the third year the plant will be mature and can then be divided if one wants to dive it.

You are in PA and the growing conditions are exelent there for peonies. Take these measures and you will have some real nice blooms next spring.