Forgive me for not helping, but you have a host that changes its IP address every 1-5 minutes?
I just need to wrap my head around this. They are using a dynamic DNS service to remap the IP address to DNS at that rate? What's the TTL they assign their domain name when it is written to the DNS provider's system?
I'm not sure what the business or technical reason for changing your IP that frequently is, but it breaks a lot of stuff (as you've discovered), it really isn't the way DNS should be implemented, and generates a lot of unnecessary DNS queries.
You're really playing a game of chase to get the current IP address. If you know the dynamic DNS service that these servers are using, I would use their name servers as your primary name servers and query them. You're at the mercy of their TTL, so if it's set for an hour, you're only going to get an update each hour unless you flush your DNS (like you're doing) in a cron job.
Again, I apologize, but I'm still trying to wrap my head around the "why" part of the implementation.