If you're using the Babbel app for Android or iOS this is possible. It's not possible if you're accessing your Babbel account at www.babbel.com via a browser.
Please remember to download the courses, lessons, and review items you want to work on before going offline.
Please also be aware that updating your operating system or the Babbel app itself will temporarily remove any previously downloaded items. All of your progress will however still be there.
You'll find links to the Babbel apps here: www.babbel.com/mobile