Not sure I understand. If you're using your ISP's DNS service, majority of your requests are going to hit their cache. You shouldn't notice any downtime as long as the cache doesn't expire.
Or you can directly ask a domain's authoritative nameserver directly. Using an intermediate caching resolver isn't required. Recursively resolving the DNS query locally only requires asking a centralized nameserver for a domain's authoritative nameservers (the NS records) which can usually be cashed locally for a long time. Every other request is compartmentalized to different servers by domain delegation.
Or do both; configure your local resolver to try recursively resolving a request, and fall back to the ISP (other) cache if needed.