The default CMS functionality does not require any external connections, unless your project has been modified or extended to make external calls in order to accomplish some scenario. For example, you can install Sitefinity on a machine that is completely isolated ( on a localhost environment ) and use the local IIS / Project Manager server / Visual Studio to host it and a local SQL server instance for the database. However if your site is using an external database server to connect to it is possible that it will not be accessible, since the CMS cannot connect to its database.
During the time the site was down, can you tell us whether any specific errors were thrown ( in the Sitefinity logs or to the frontend / backend user ) ?
the Telerik team
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system and vote to affect the priority of the items