@Lilley, Kristopher L Apologies for the delay here! That makes sense.
While there is no built-in way to do this, the SDK does do some caching which you can control with the SetCacheExpiration method but is still not a persistent way of doing this.
I suppose the alternative would be to manually persist the current configuration into a file and use that as a source if Azure App Configuration is down/inaccessible.
That being said, I would suggest creating a feature request for this to have the team consider it in the future.