What is the recommended snapshot age in Nutanix?

It’s less about the recommendation from the Nutanix perspective as it is what you need from a business perspective.  Nutanix can keep a snapshot as long as you like with how it does snapshots it doesn’t impact performance.  Question is how far back do you want/need to be able to go back and at what point is the data no longer valid if restored.

Is there an expiration date?

No. 

But there is a NCC that will check how long the chain is. (max 35 snapshots). https://portal.nutanix.com/page/documents/kbs/details?targetId=kA0600000008fWbCAI

You can set how long you want to keep them when you setup your protection domains/policies.  You can keep X number of hourly, Y number of daily, Z number of weekly and setup your strategy that way