No good news to add. Got my mini iPad last December. Service on Verizon. 2GB of data and only use half of that/month. Have gotten the "No data left on cellular data plan" message and option to add data every month, always on a date that is within a few days of the monthly billing cycle data. Has happened every month since getting the iPad. This month, I have been getting the message frequently vs. only at the billing cycle date.
Apple has been great over the last 7 months. They have done the following: replaced the SIM card, reset network settings (multiple times), given me a new iPad, restored the new device several months later, and most recently, reprovisioned the account. Nothing has stopped the messages.
I have also contacted Verizon multiple times over the last 7 months. Both last month and this month, Verizon seems to have info in their system that indicates this is an Apple software issue that they have acknowledged. There is no info on timing for the resolution. Verizon says they have 1.5 million devices reported as having this problem, which I think is a very low number and likely will not drive a high priority with Apple, if the issue really is an Apple software issue. Apple reports no knowledge of a software issue.
On my own, without suggestion from Apple and Verizon, I have discovered that shutting the device down and restarting will resolve the problem, but as noted above, this is a termporary fix. Until this past month, the shutdown/restart solved the problem for me until the next monthly billing cycle date. Now, with the more frequent messages, the shutdown/restart still works but it is not for the full month. While the shutdown/restart is a hassle, it at least fixes the problem so that I can send and receive messages. But given the increased frequency of the message, it is becoming really annoying.
I have asked Verizon to provide me more about their info that says this is an Apple software issue. Verizon apparently has an internal forum and the moderator has communicated with the forum that this is an Apple software issue. I have asked the Verizon rep to go back to the moderator and find out where that person got this info. If the rep can provide me that info, I plan to share it with Apple since all of the Apple tech service reps I have worked with (both on the phone and at the Genius bar) have not seen or heard of this problem and are unaware of what Verizon is saying.
If I learn anything new, I will share. But for now, we all seem to be stuck with a very frustrating problem for which there is no solution in this electronic age when such hassles should not exist.