As far as I know, the Persian nations to the east of the early-middle Roman Empire were the only states bordering it which were of any military or economic worth. Yet even the Parthian and Sasanian Empires only controlled Persia and parts of Central Asia, the Caucasus, and Mesopotamia. The Roman Empire, on the other hand, was... the Roman Empire. Are these two nations really considered rivals? Did the discipline of Persian troops compare to the Roman legions? Were the Persian states able to produce a more centralized government due to their smaller size? What other advantages, if any, might they have had?
One of the most widely-accepted reasons given by historians as to why Parthia/the Sassanids were never conquered by the Romans was that the Roman Empire was at its geographic peak and could not be expanded any further without serious problems with what I suppose could be called "national security".
Many Emperors campaigned successfully against the Parthians/Sassanids -- those of note include Trajan, Lucius Verus (co-emperor with Marcus Aurelius who campaigned in the West), and Septimius Severus (father of Caracalla), among others. Most notably, the Empire reached its geographic height in the last months of Trajan's reign (117 AD), where he had conquered modern-day Armenia and the eastern Levant (his conquered lands actually reached up to Kuwait and the shores of the Persian Gulf). Almost immediately upon his death, however, the Empire had to give these provinces up. The strain on the treasury and the simple bureaucratic mess it was to rule these provinces effectively meant that it would seriously compromise Rome's political stability and would make her borders more porous. It must be noted that it would take quite a lot of time for an Emperor to travel from Rome to Ctesiphon (the capital, in Mesopotamia, of the Parthian Empire) in Antiquity; and since the greatest Antonine (mid-2nd century) Emperors usually campaigned themselves and led their troops in person, it would be quite difficult to be that far from home while also managing the administrative affairs of the entire Empire and dealing with military affairs in other regions, like Germany or Britain.
The Parthians and Sassanids were the only other contemporary peoples in the history of Rome that were never truly conquered, who had an established bureaucracy and political tradition, and who could effectively be considered a "nation". This differs from the barbarian tribes in that they were mostly migratory, usually lacked political cohesion (except for adherence to a tribal chieftain or petty king), and could not nearly be considered a settled, sedentary people.
The peoples in Persia certainly benefited from lying directly along the Silk Road, which was a major source of trade for the Romans with the East (read: China). They also didn't have to deal with the enormous numbers of migratory peoples pouring through their borders in the 3rd, 4th, and 5th centuries (except perhaps for the Sassanid invasion of the Parthians in the 3rd century).