Egypt remained "special" throughout the period of rule from Rome (through at least 395, in some respects through 640), and there is no indication that the Augustan restrictions were ever lifted.
Dio recounts in the Roman History 51.17 that
[Octavian] made Egypt tributary and gave it in charge of Cornelius Gallus. For in view of the populousness of both the cities and the country, the facile, fickle character of the inhabitants, and the extent of the grain-supply and of the wealth, so far from daring to entrust the land to any senator, he would not even grant a senator permission to live in it, except as he personally made the concession to him by name.
Tacitus tells us in Annals 2.59
[Tiberius sharply rebuked Germanicus] on his visit to Alexandria without the emperor's leave, contrary to the regulations of Augustus. That prince, among other secrets of imperial policy, had forbidden senators and Roman equestrians of the higher rank [equites inlustres] to enter Egypt except by permission, and he had specially reserved the country, from a fear that any one who held a province containing the key of the land and of the sea, with ever so small a force against the mightiest army, might distress Italy by famine.
Augustus tells us in Res Gestae 27 that he made Egypt a domain of the Roman people— in contrast to a province of the Senate. In practice, his victory over Mark Antony and Cleopatra had given him direct control of Egypt and its immense wealth; he ruled as if a pharaoh. Egypt was both an important source of grain and easily defended, making it particularly valuable and to keep out of the hand of potential rivals.