The South African money is losing a lot of its value and media are very pessimistic. What can i do in order to avoid my savings being worthless in a few months ?
Use other currencies, if available.
I'm not familiar with the banking system in South Africa; if they haven't placed any currency freezes or restrictions, you might want to do this sooner than later. In full crises, like Russian and Ukraine, once the crisis worsened, they started limiting purchases of foreign currencies.
PayPal might allow currency swaps (it implies that it does at the bottom of this page); if not, I know Uphold does.
Short the currency
Brokerage in the US allow us to short the US Dollar. If banks allow you to short the ZAR, you can always use that for protection. I looked at the interest rates in the ZAR to see how the central bank is offsetting this currency crisis - WOW - I'd be running, not walking toward the nearest exit. A USA analogy during the late 70s/early 80s would be Paul Volcker holding interest rates at 2.5%, thinking that would contain 10% inflation.
Comes with significant risks itself, but if you use it as a temporary medium of exchange for swaps - like Uphold or with some bitcoin exchanges like BTC-e - you can get other currencies by converting to bitcoin then swapping for other assets. Bitcoin's strength is remitting and swapping; holding on to it is high risk.
I think these are higher risk right now as part of the ZAR's problem is that it's heavily reliant on commodities. I looked at your stock market to see how well it's done, and I also see that it's done poorly too and I think the commodity bloodbath has something to do with that. If you know of any commodity that can stay stable during uncertainty, like food that doesn't expire, you can at least buy without worrying about costs rising in the future. I always joke that if hyperinflation happened in the United States, everyone would wish they lived in Utah.
Transfer your savings to a dollar-based CD. Or even better, buy some gold on them.