We were experiencing a lot of breaks with the API connection of GTW over the last week or so, as well and something like this would have been very helpful.
Interestingly, there is already the Notifications log, which lives in the top menu bar next to the Admin/Account/Help buttons and even offers the 'subscribe' functionality. So it would seem that this functionality already exists.
For some reason, though, this notification log doesn't seem to pick up an API disconnection, even when filtering for Web Services in notification types (see screen shot). Knowing that we had many disconnects recently, I would expect them to pop up here, so maybe it's more an issue of making this log more robust.
This still seems like a blind spot in the alerting architecture. It's extremely concerning that something like a LaunchPoint service can just fail silently and that it's left to someone seeing the downstream effect of the breakage to reconcile.