Is there a known problem with SMS notification to Verizon Wireless users?

Several times in the last two days, when I load the Twitter home page http://twitter.com/home, I see a red notification box: "Is your phone okay?" It tells me notifications have been turned off to my phone because of some problem with delivery.

My phone is receiving and sending text messages from all other sources without problems, and tweets I send to Twitter from my phone go through just fine. I have turned on phone notifications four times now, and I know of at least one other Twitter user who has a Verizon Wireless phone and has experienced a similar problem. But a few hours after I turn notifications back on, I load the Twitter home page and see the red banner again, and have to turn notifications on once more.