replication – Failover and DNS propagation delays

When a DBMS fails over after a failure, if it fails over to a server in a different and unrelated data center, then the IP address of the subdomain name of that database will need to be changed in that name’s DNS server, and due to DNS propagation delays, it could be days before all the DNS servers of the world have the IP address for the new master, during which time some clients would still be trying to access to old master. What can be done to deal with this, other than changing the client software to fetch the IP address of the master from somewhere, or is that the only option? Thanks.