The short answer is: nothing.
We’ve built Screenly Pro from the ground up to survive network outages, which is really the same as if our servers were to go down. This is an important feature, in particular if your nodes are using a 3G connection for which network disconnections are common.
The only consequence of a node losing its connection to our servers (for any reason) is that it cannot retrieve updates to assets and play lists. The screen will still keep showing the material last retrieved.
Beyond that, the nodes keep a playlist with the start and end time stored locally (along with the asset, if it is cachable). As a result, assets will still expire and stop showing as scheduled, as long as that expiration time was known at the time of the last sync.
Finally, it’s fairly unlikely that our servers would go down for any longer period of time. We have many years of experience running web services and we apply multiple measures to ensure the high availability and uptime.