14 days — informal challenge in the discount window
From the date the PCN was served on the vehicle, the discount period is 14 days, and you can make an informal challenge within it. (If your council PCN came by post — for example from a camera — the steps can be different: it may already be the formal notice, with no separate informal stage, so follow the steps and deadlines printed on it.) If a challenge made in that window is refused, the Government's statutory guidance for England recommends the council consider re-offering the 50% discount for a further 14 days — a recommendation, not a guarantee, so check what your council says.
28 days — formal representations after the Notice to Owner
If the informal challenge is refused (or you skip straight to formal), the council issues a Notice to Owner (NTO) within 6 months. From the date the NTO is served, you have 28 days to make formal representations to the council.
28 days — tribunal appeal after Notice of Rejection
If your formal representations are refused, the council issues a Notice of Rejection. From its date you have 28 days to appeal to the Traffic Penalty Tribunal (or London Tribunals in London). After this deadline the council can issue a Charge Certificate and the right to appeal is gone.