So, interesting (to me anyway).
I did another sync to the site, and it said I needed updates (which surprised me since I just updated 15 minutes or so ago). This time it updated my contacts/messages/etc., but did not do any more firmware upgrades. The flashing red light was now off.
So I took it outside and asked it to check for new messages, and in came the reply to the test message I sent 15 minutes ago.
Sent another test message (there's 3 of my 5 for this month! :-). Didn't get an immediate reply, but did get one when I asked the device to check for new messages. And flashing red light continues to no longer be flashing.
Seems to be fine. So maybe you just need to sync twice for some unknown reason, once to upgrade the firmware and once to update everything else.