I have the same issue with three separate phones. I've also discovered the "preventive" approach -- adding a new text package a day or two before the old one expires. To do this effectively you should turn off auto renewal on the web site several days beforehand.
Then, use the phone interface (rather than the web interface) to renew. You can call 611 from your phone or call 800-901-9878 from any phone. This seems to work much better than the web site. They basically runined the web site a few months ago and it really hasn't been the same since.