You could run a local resolver like dnsmasq or Unbound that can “serve stale” on upstream failures, but that assumes the DNS failure is a client-facing resolver one.
From what I observed here, it was more internal DNS related: Newegg was serving an opaque “DNS failure” error page from Akamai’s front-end which is likely because their infra was failing to resolve names internally.
Unbound has a 'serve-expired' option: https://nlnetlabs.nl/documentation/unbound/unbound.conf/#ser...
Basically soft-invalidate your local DNS cache but it back from the cache graveyard if DNS is down.