There are two different types of progress being saved going on at Free Code Camp: your profile and your browser cache.
Your completed challenges are all saved to your account in the FCC database. You can see the list of completed challenges and also the last submitted solutions by looking at your profile page.
Your progress tracking (map) is saved in your browser's local storage. In-progress code is also saved in your local browser cache. If you are changing browsers or clearing your cache regularly you'll have to use freecodecamp.com/map to navigate to your next challenge. Especially as you get to more complicated challenges that may take multiple sessions, I strongly recommend saving your in-progress work outside of the browser cache. This is a good opportunity to learn the ins and outs of your GitHub account, but you can also just save locally or use a service like repl.it which allows for versioning.