There is no general extension process if you miss it. The Board of Revision hears appeals filed inside the window on the notice, and a late filing is typically refused outright rather than reviewed on its merits, which is a harder outcome than most homeowners expect from a municipal process.
Because the clock starts at the notice date rather than a fixed calendar month, two neighbours whose notices arrived a week apart can have deadlines a week apart too, so checking your own notice is the only reliable way to know your specific date rather than relying on what a neighbour or a general answer says.
If you plan to appeal, gathering comparable sold prices before the deadline, rather than after, gives the Board of Revision something concrete to weigh. Get your hand-reviewed valuation from Joel Dyck.