A bug present since version 1.0 of DragonBox/DragonBox+ could prevent you from accessing an island even if you have completed all preceding levels with 3 stars. The issue was fixed in release v 1.2.0 in February 2014. If the issue still persists please make sure you run the latest version of the game, and contact support.
A known workaround is to re-play the last level of the last unlocked island so that you earn again the 3 stars. This should unlock the next island.