Motorola Defy Plus - Apps are automatically closing few minutes after screen switches off
Go to task manager icon from round lighted main icon at bottom center of phone. Once task manger is running , click on auto end list and remove your connect music app or any other app that plays music. Thats it.

Also notice before you do the operatino above that musics would stops playing after about 2 minutes. Because that is the default setting for the auto end list in the task manager app.