I'm not sure it really expires during the main tax season....but the base price that Intuit charges, from which the discount is applied....that base price usually increases ~1 March.
So...you can get the full discount by paying for your Fed&State tax form sets before the end of February, even if you don't file right away
.....but always check your filing fees before purchasing....sometimes you have to revisit the Fidelity web-page access point to re-initiate some kind of background cookie that applies the discount.