At some point, the interests of the people of SD would best be served by appointing at least an interim successor, to hold the position and vote, either until the end of the term, or until the current Senator recovers.
There may be no provision for an interim senator, meaning awaiting for the return of the ill member. I don't think the Constitution addresses this, as I recall, not having checked into the particulars. I would imagine thqt the Democrats would force the SD governor to name one of their own if he must appoint.
Only one senator per seat. Johnson retains it until he dies or resigns regardless of effectiveness.