Wont Change Name on Ticket, Flying to CT when Ill

SAA seem to be the only Airline that wont change the Name on your ticket. The company I work for booked me to fly to Capetown. I got sick since the flight was booked. I have a doctors note and was booked off work. SAA will not change the name on the ticket so that someone else can fly down in my place even when a doctors note is supp****. My options are either we book another flight for someone to take my place and pay for the ticket that was booked for me or I fly down with gastroenteritis (Flu coupled with the ****s). I can think of nothing worse and am sitting here contemplating whether I'll cover the cost of my flight or just try and deal and fly down. Either way SAA's policy on this is ******** and I feel it should be changed and if I just let this go someone else will also get *****ed in the same way I was.