At the moment, its rather difficult to recover from a network interruption that happens when you send the request to Xero API, and you loose the connection before you receive the response from Xero. There is a fair number of reasons why this could happen at any time.
In such a situation you really have no way of knowing if your request was even sent fully, or if it was received by Xero, nor what was Xero's response.
This is not specific to Xero, as all APIs out there have this same problem, as its simply how the web works.
Best solution to this I've seem so far are Idempotent Requests.
With each request to Xero API you would include some kind of a unique identifier which only needs to be unique to you, not all of Xero users. For example if you need to send some invoices to Xero and you have each of them already saved in your database, you could send your primary key as your unique identifier as this is something that will not change on your end.
Xero then reads your request and makes a note of what was requested and saves your unique key along with request params.
If network goes down at this point, Xero will still know what you requested and prepare a response for you, but will not be able to deliver the response since the network connection is closed now.
To retry, you just send the same request, with same unique identifier and Xero knows you already requested that, and just returns the cached response, that is was unable to deliver last time.
In another scenario, if your network goes down even before Xero received your request, next time you send the request, it will be a new one for Xero, and it will be processed as usual.
So in both cases, when network goes down before and after your request was received by Xero, its safe to retry your request once network connection is restored.
Stripe is a nice example of an API that supports idempotent requests, which makes working with it much easier and worry free.
If you were to try to achieve something like this now, it will not only be impossible to do in all cases, but it would also take a lot more of your time, be much more prone to bugs as you would need a separate system for each document type in Xero, plus it would eat into your rate limit as you would need to query the API first, before you can try sending your request again.
Sean Tomlins commented
This causes us real issues where we are having to explain to our customers why there are duplicate invoices created in Xero when there is a network issue