If this happens, you need a HomeKit hub for remote access. When you're home, your phone acts as a hub for HomeKit. When you leave home your hub comes with you, leaving no way to access your thermostat via the HomeKit app. You can verify that your thermostat is still connected to the internet by looking at the Mysa app. There you will be able to see the connection status of your thermostat.
The good news is you don't need to buy a new device. Your HomePod, Apple TV 4K, Apple TV (4th generation), or iPad (with iOS 11 or later) will do the job.