Did they say why they are making that distinction? After doing a re-sit, your course end date has now been extended to 1 September, so I can't see any specific reason why they cannot issue a CAS for the extension. If it is the university's own internal policy, it seems a strange one that could shut down the option of the Graduate route to many of their students. They could have a riot on their hands.
I advise asking the International Student Adviser to help you appeal this. You may find that there are other students in the same position, which could help your case.
There is still the possibility to apply for an exceptional assurance if your permission ends on or before 30 September, but this is specifically for people who cannot leave the UK at the end of their permission, due to pandemic-related reasons:
https://www.gov.uk/guidance/coronavirus ... -residents
I do not give immigration advice. I refer you to Immigration Rules, guidance, other online content and to your sponsor.