I posted a ticket, but I'll post the attachment here too:
And I'm running another ping test now, as well (many apologies for taking the screenshots with my phone this time around):
I didn't see any of the General Failure messages yesterday, but today they're happening roughly within 2-3 minutes of each other (I still have the test running, and they're still popping up every so often...not as frequently as the request time outs, but still).
Addendum: Okay...I still have it running, and I just saw two "Destination host unreachable" messages from my IP address within maybe 30 seconds of each other.