With a SYNC XSite replication it is possible to automatically mark a site offline with the following configuration

<distributed-cache name="XSiteCache" ....>
...
<backups>
<backup site="site02" failure-policy="IGNORE" strategy="SYNC">
<take-offline after-failures="10" min-wait="60000"/>
</backup>
</backups>
</distributed-cache>

If the strategy is ASYNC (i.e. for performance reason) the element take-offline will have no effect as the site will 'fire and forget' the updates and don't care about failure.

It should be possible to use the take-offline configuration in ASYNC mode as well