If they still don't accept my appeal, I will have to pay £70 instead of £35.
No, it's not up to the council to decide whether you have to pay or not. If the council rejects your representation, you can appeal to the Traffic Penalty Tribunal.
In any case as long as you challenge the Notice to Owner promptly the council will reoffer the discount, because they want to give you a discount not to appeal to the Traffic Penalty Tribunal.
If you have to appeal to the tribunal, I'm happy to act as your representative. We don't advise to appeal unless we think you're likely to win.