I just got a response back from them. They think, and I tend to agree, that it is Timer issue. They suggested checking the SIP registration timers.
I used the Obihai defaults for the Broadvoice configuration.
Broadvoice said they will check their logs to verify that it is not something on their end. I don't think it is, as I use a Broadvoice-supported device that works fine.
Also, as I had mentioned, I am not experiencing any Internet connectivity issues.
I will post more when I hear back from Broadvoice tomorrow.