Not my experience at all, at least with pourovers. Others have done blind taste tastes with beans upto 6 months out from the roast date (light roasts), which seem indistinguishable on pourovers and immersion brewing. The taste tests suggest that peak flavor develops at about a week out from roasting, and degrades very slowly - much more slowly than conventional wisdom suggests. The norm has been that beans are essentially stale 2 weeks out from roasting. These tests suggest that as long as you store your beans reasonably well, they're good for several months. Depending on your technique, the loss of the bloom might require modifications, but they're still good beans.

I can imagine that the same probably doesn't hold true for espresso, since the back pressure from out gassing is crucial to extraction.