When the authoritative server (an authoritative DNS server is what you call the "main" DNS server in your question; it establishes what IP, say, some-name.example has) goes down, the caching server (a DNS server that gets its information from authoritative servers) will only have in its cache names that have recently been requested.
So, supposing that your authoritative server has a TTL of 1 day for its records, when the auth server goes down, any records retrieved in the last day will be around for under one day and then stop working. Any records not fetched in the last day will not work.
The purpose of DNS caching is simply to speed up resolution of names. DNS' way of making records reliable is by using something called a "DNS zone transfer", where the "main" server becomes what is called a "master" server in DNS. The one sets up a second "slave" DNS server that periodically gets its DNS record from the "master". More information: http://www.microhowto.info/howto/configure_bind_as_a_slave_dns_server.html