Bukkit does not support it so you need to do certain things. You probably should be connecting from a legit account but I will tell you how to fix it. You know that batch file you use to open up your bukkit server? You need to edit it. Change it from:
java -XmxXXXXM -jar craftbukkit.jar -o true
java -XmxXXXXM -jar craftbukkit.jar
Just remove the -o true in the file and set your online mode to false again.