Multi-site support: HST connection error message doesn't show the problematic site

Situation: In the testsuite bring down the intranet site while logged in on the CMS.
In the Channel Manager the error is shown: The connection to the HST timed out. Do you want to retry to establish a connection?

Expected: An error that indicates which site is the problem. If not possible at least word it to something like 'The connection to a site timed out.'