Major crises affected the Empire from 235 to 284 CE. The basis of the crises was increasing pressure from foreign invaders on the Roman borders coupled with political instability within the Empire itself. The emperor Severus Alexander was murdered in 235 CE. All of the emperors to follow for the next fifty years were murdered or died in battle as well, save one; there were twenty-six emperors in those fifty years, and only one died of natural causes(!) Many emperors stayed on the throne for only a few months before they were killed. Not surprisingly, in this environment, most emperors were only concerned with either seizing the throne or staying alive once they had it, meaning they tended to neglect everything important to the stability of the Empire.
Rome’s internal political problems were somewhat of its own making - the Praetorian Guard auctioned off the throne, would-be emperors eagerly assassinated their rivals, and Roman elites largely retreated to their enormous estates to profit off of their serfs. Other factors, however, were external: Rome's international environment grew much worse. In 220 BCE, a new clan - the Sassanids - seized control of Persia. The Sassanids were much more aggressive and well-organized than the earlier Parthian dynasty had been, and Rome was obliged to fight almost constant wars to contain the Persian threat. Simultaneously, the barbarian groups along Rome's northern borders were growing larger and better-organized. Centuries of contact with Rome itself had improved agricultural techniques among the barbarians, leading to population growth. Eventually, these larger, wealthier groups joined together into forces that posed serious threats to the Roman borders.
As the quality of Roman leadership declined and the threats grew worse, the results were predictable: Rome lost battles and territory. The emperor Valerian was captured by the Persian king Shapur I when he led a Roman army against Persia and, according to some accounts, was used as the Persian king's personal footstool for climbing up onto his horse. Another emperor rebuilt walls around Rome itself in 270 CE because of the threat of Germanic invaders from the north, who had pushed all the way into northern Italy. Likewise, emperors, all being generals at this point, traveled constantly with their armies and made their courts wherever they had to while waging campaigns.
The problem was that the entire Roman imperial system hinged on the direct, personal decision-making of the emperor himself. The emperor was supposed to oversee all major building campaigns, state finances, and the worship of the Roman gods, not just military strategy. Thus, in an era when the speed a message could travel was limited by how fast a messenger could travel on horseback, the machinery of the Roman government ground to a halt whenever the latest emperor was weeks or even months away from Rome. Needless to say, the problem was exacerbated when the Empire was torn between rival claimants to the throne - for a few years toward the end of the crisis period the empire proper was split into three competing “empires” under rival imperial pretenders.