It's weird since DNS is one of the most rock solid systems we have, with redundancy at every level.
1. Clients query a list of servers (IPs) and handle failover when you don't quickly get a reply.
2. Most of those servers at the root and TLD level are actually anycasted from multiple locations globally, so you connect to the closest instance.
3. Those instances are often clusters of physical servers. The big ones have fully redundant networking, so any router or switch failing doesn't take it down. Some run different DNS server software on each physical server, so even software bugs won't take down the whole system.