An error occurred while saving the commentMark VB commented
A very simple solution to archiving message is to install an app designed specifically for this propose. I use "SMS Backup +" to folder all my message into my Google account. It allows me to save and delete any messages or threads that I desire. And, using Outlook w/ IMAP to my Google account, I can sort message into conversations making retrieval or deletion of threads much easier.
I don't believe MightyText is intended to be an archive of all you text message. It's a web interface that allows you to communicate via SMS when your phone is not readily available or when you desire a full keyboard to communicate. In my opinion, It achieves this purpose very well as it is designed and I too would like to see message deleted from my phone deleted in MightyText.