A South African law contract comes into being when an offer to contract is accepted by the other party. If the response does not accept the offer according to its specific terms but suggests changes, this is a counter-offer. The offer itself is considered rejected and lapses. This is South African law as well as UK law (we all harp back to the ingenious Roman law of contract).
The UK have codified rules regarding special types of settlement offers. An offer made under Part 36 of their Civil Procedure Rules remains open until it is withdrawn and is not extinguished if there is a counter-offer. Our procedure for payments into court as a settlement offer is similar.
It is not a bad idea when making a settlement offer to leave it open for a reasonable period. The offeree can be told that the offer will remain open for that period even if it is rejected or countered during that period. It puts more pressure on the other side and shows good intent in any argument on costs.