In a very similar set of facts our High Court recently had to consider whether a municipality could provide an extension of time for an appeal to a party beyond the 21 day time period allowed for by the Municipal Systems Act 32 of 2000 which regulates the conduct of municipalities.
In deciding on the matter the High Court found that the municipality, as an administrative authority had no general power to create an exception for a party who had failed to comply with the unconditional statutory time period where the statutory provisions did not create scope for exceptions to be made. Accordingly, despite the merits of whether an appeal should be considered, the fact that the appeal was submitted late could not be condoned by the municipality and the municipality did not have the power to make an exception and allow a late appeal.
In your situation, it therefore sounds as if the same principle may apply and that despite your perceived merits in believing you have grounds for an appeal, the above principle will not allow your municipality to consider extending the period for the lodging of an appeal.
Government procurement however remains an intricate area and it is advisable that you obtain specialist legal advice before deciding on any specific course of action in this matter.