According to this Wikipedia article: https://en.wikipedia.org/wiki/Military_tribune "an Augustan law required that no member of the Senatorial Order ever enter Egypt." The wiki article cites this book: Legions of Rome as being the source for this information, but in the 'look inside' the page cited does not have any information about this law.
The Britannica Article on Ancient Rome states: "An entirely exceptional imperial province was Egypt, so jealously guarded that no senator could visit it without express permission." (The Consolidation of the Empire under the Julio-Claudians -> Administration of the Provinces)
Why was Egypt so 'jealously guarded' by the Emperor? Was it entirely because of its status as 'the breadbasket of Rome'? What could one Roman senator accomplish if simply allowed to be present in the province? Are there any known instances of senators receiving permission to visit, or violating the law and showing up in Egypt?
/u/XenophonTheAthenian might be able to shed some more information, but, prima facie, we do not know, or cannot be sure, as for the reasoning, either initially, or why the tradition of equiterian prefects was kept later on. And it was not merely senators, but more generally equites inlustre, which is not strictly defined and varies in usage.
The common reasons of senatorial distrust cannot be all that pervasive, since Egypt had by the AD 20s two legions, further reduced to one later on, when senatorial legates had much stronger armies much closer to Italy, so reasons given by Tacitus and Dio are not taken as all that plausible, and since there are also instances were Egyptian prefects joined the rebelllions of legates, and further, given the numbers of the executions in the first hundred years of equites, there is little indication that equites were throught of as more trustworthy. So is the reasoning that Egypt at the late Republic and early Principat was of vital economical important likewise does not hold up, and was an anachronism, but granted, later Egyptian economical role though did expand, so by 69 AD, we have Vespasian thinking of starving Rome by blocking the Egyptian export.
Likewise, we cannot know why Cornelius Gallus was chosen as the first equiterian prefect, though intial familliarity with the province and adminstration might be the reason here, or at least during the first decades, it is not true for later appointments.
/u/XenophonTheAthenian might be able to give you some names of more exceptions, if there are any, but I know in the 3rd century Macrinus sent a senator to administer Egypt. ( Edit, also /u/LegalAction. )
Brunt, P. A. (1983). Princeps and Equites. Journal of Roman Studies, 73, 42–75.
R., Meyer. (1988). From Republic to Principate: an Historical Commentary on Cassius Dio’s Roman History Books 49-52 (36-29 B.C.)