RCollins: we have experienced the same when using text-to-SMS. While reading the Twilio reference pages, we came across a clue that seems to have improved our text-to-SMS message delivery success rate (reduced blocking).
Mobile carriers are always working to reduce SMS spam and they scan every SMS message. One of the content items their filters look for is any reference informing the message recipient of how to stop future messages from . the sender. One of the key works is "STOP". We now include an end of message phrase of "Reply STOP to unsub". This has nearly eliminated message blocks that were mostly done by T-mobile. The cost of using the phrase is fewer characters available for other content.
Twilio is a fine service though along with the added cost they have created a "corn-maze" of rules, requirements, and verifications (to limit spammers) that can cause frustration. As of early November the verification rules will tighten further.
Your mileage may vary...