Was the move due to the decline of the city, or did the city decline because of it?
Did the city become more isolated and unimportant, or was it still a major center?
Did this move lead to it being more vulnerable to the sackings in the 5th century?
To clarify, I'm interested in the period 286 to 476.
The move was idea of Diocletian when he decided to set up the tetrarchy, each emperor had it's own capital. Augusta Treverorum was the capital of Constantious Chlorus;Mediolanum the capital of Maximian; Sirmium the capital of Galerius and Nicomedia the capital of Diocletian. Rome didn't lost the title of the imperial capital but it lost a huge power. Diocletian died in 305 and the tetrarchy was over. Then Constantine became emperor after the victory at the Milvian Bridge and decided to centralize the power again in Rome, but not for long. Rome was affected by the empire's instability, that's why Constantine chose a new capitol because it was safer than Rome (Being in Rome would have meant constant opposition). By the end of the IV century Rome declined from a population of a million to 30.000. Yet it still had a historic and moral importance for the millions at the empire. As the empire was divided and Rome became less safer the emperor move the seat of the government to Ravenna, yet the senate was still at Rome. The 410 sack was a major shock in the entire roman world, the city that conquered the world had been sacked. Major monuments were not damaged and Alaric ordered churches to be spared but Rome became impoverished and lost more population. The 455 sack didn't helped but at least it mantained it's greatest monuments, for example, the Baths of Caracalla were still in use at the VI century.