Not sure I totally understand what the problem is, but check these steps..
You have a Twilio SID and token saved in Church Admin
You have a user account connected to your directory entry
You have put your name as the one to get push notifications on the app when a SMS reply comes in.
Are you getting the SMS in your phone message app?
You are getting the Church Admin push notifications, but are you saying you sometimes don’t get anything in the SMS replies section of the app?
Are you saying the SMS reply section of the Our church app or website is not working for you?
There does seem to be a new bug when replying from phone SMS app – where it is not showing in the Our Church app SMS replies thread, when notification is touched. But it does show in the SMS replies page of the Our Church App. Will look at that