I wanted to post this here, in case anyone else runs into this and scratches their head as I did.
I had paired my account with Twilio and was able to send and receive messages just fine; however, my sms auto-reply trigger would not work. Eventually, I came across a mention of the SMS channel using notifications to send things from triggers or the scheduler. Lo and behold, that was the missing link; one has to enable SMS Notifications in the SMS module for the auto-replies to work.
I did not think notifications would be the case, as this was not so much a notification as a reply, yet here we are. Hopefully this saves someone else a bit of time. 