If you are having issues with conversations or messages missing from your conversation list after you log in, then Resync messages is the solution for you. The Resync Messages option works differently depending on what device you are using. It is available in My Account > scroll down to Danger Zone > toggle on.
On a primary (phone) device, it will delete all the messages that are saved for your account on the web, then go through the initial import from your default Android Messages app - (like when you installed the app for the first time) - and push those imported messages up to your web account. On a non-primary (tablet) device, it will clear out Pulse SMS's local database and download everything from the web.
Please check your default Android Messages app to make sure that all of your conversations are there before selecting Resync Messages option. If you are missing conversations on your Android Messages app, do not proceed.