This is most likely occurring because your Live Sync Draft Assistant is not refreshing.
You can manually refresh by clicking the "Refresh" button in the upper right corner of the Draft Assistant before each of your picks. This will pull in the latest draft data. You can also click turn on auto-refresh to update draft information every 20 seconds.
Another reason why this issue may occur in the Live Sync Draft Assistant is because keeper data wasn't added or updated in your Draft Wizard league settings. Failing to have the Draft Wizard's keeper data match that of your league will result in the Draft Assistant seeing keepers as available players.