I've had friends from neighbouring countries who completed their in service training in South Africa. They had a little more trouble finding the ist than us locals however they did complete their studies. Perhaps i could ask them how they did it you'd like me to ask..
I did a little digging. I expect that internships are considered normal work, so you should be allowed, but only to a max of 20 hours a week.
Student visas in South Africa allow students to work while pursuing their studies. However, international students may only work up to a maximum 20 hours per week. The student can work part time till the expiry of the student visa and not after.