This could be this same issue as the one reported here:
The tray menu is actually a separate process (odrive.exe) than the main odrive app (odriveapp.exe). We have seen that having a lot of items in one or more of the “lists” that the menu keeps track of can cause unresponsiveness.
The next time you see this happen, can you run the commands listed in the post I references above? It will allow us to see if odrive is still running and the tray menu is the one with the problem. If so, it may also reveal why.