Article I, Sec. 3 says that "No Person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen."
Cochran was a resident of Mississippi when he was first elected senator. It doesn't say anything about re-elected senators having to maintain their residence in their state.
I’m not talking about the legal issue. Since the popular election of Senators started, its thrown the structure of the Constitution off balance. The States created the US government and now they have no voice in the Federal Government. They’ve become just administrative divisions of the Federal Government carrying out the edicts. Just think of Common Core, Medi-Caid expansion, highway trust funds, Head Start, Food Stamps and a zillion other actions legal and illegal.