Well, it's a common issue now... South Africa permits tourists to stay only 3 months per year in the country and that's not enough for a lot of us. After all, SA is the only country in the continent where we have such an easy access to spare parts and services that you struggle to find in the rest of Africa. So, it's your best bet to take care of your vehicle, yourself, paperwork etc.

I've met quite a few overlanders who overstayed their entry permit but now I have my own story to tell, which had a happy end after all...
Extending the tourist permit is practically impossible. According to the law which is valid since May 2014, I was declared undesirable in South Africa, since I overstayed. There is no fine anymore for that. The only issue was that when I was exiting South Africa, the friendly officers at the border were worried that I would be in trouble if they would not grant me a visa for Botswana, since I would be stuck between the two countries. Initially, they wanted to send me to an airport and make me fly back to my country! Happily, when I explained them that Europeans do not need a visa for Botswana, I convinced them to give me the documents which declare me undesirable for a year and let me go though the border. If you overstay more than 30 days, then you will be declared undesirable for more years. They did not write anything about that in my passport.

More info at:
Madnomad: Southern Africa - mad nomad

Hope it helps!

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Asia, 27 months, 73,000 km. - Africa, 3 years, 96,000 km. - Honda XR 250 - http://madnomad.gr