A persistent offline desktop app
The offline support in Todoist is fine for getting you through a brief network outage. But you've got to have *started* online, as near as I can tell. If you've boot your laptop out in the woods without a network there's no way to get to your lists of tasks. The existing Mac desktop client appears to be nothing but the web client in its own window, and has the same behavior with respect to network connectivity as Todoist in a web browser. Similarly, the Chrome plugin, while adding a few more integration features, still requires a network connection to get it started, and is really just the web client with the added bells and whistles.
The iPhone client, on the other, launches just fine when there's no network (wifi or cellular), simply using what it's most recently cached from the server. It would be great to have something similar on the desktop. And well worth a premium subscription to get.
This is a current limitation of the platform we use (HTML5). It's fairly new and some things are hard to pull off.
We are aware of these issues and we will address them in the future when the technology permits it.
For now, the best thing you can do is to have Todoist always open.