Oftentimes, a reading history sync problem can be fixed by logging out and in again to the app. If the syncing problem is between the website and your mobile device(s), make sure that you're running the latest OS on your device(s) and that you've installed the newest Blinkist app version.
You can also force a sync to your mobile device (Android only) by visiting the 'Settings' page and clicking on 'Synchronize'. For more on this please see here.