I noticed this some while ago while looking through entity AI related stuff.

In the original commit which added support for changing the rabbit type (https://hub.spigotmc.org/stash/projects/SPIGOT/repos/craftbukkit/commits/2db3ea29a650c045fdaf155d636dbd77a07fa21f) the rabbit's AI goals got reset whenever the rabbit type gets changed from the killer rabbit to some other rabbit type.

During the update to MC 1.9 this resetting of the AI goals broke: https://hub.spigotmc.org/stash/projects/SPIGOT/repos/craftbukkit/commits/aa008dff0f9bedbe88e1fe79831776b0a52eb90a#nms-patches/EntityRabbit.patch

In the current state, the rabbit converted from the killer bunny to some other type of bunny does not regain its original behaviors and stops moving around.

The rabbit will also retain its custom name and increased armor attribute, however one could argue that plugins can be responsible to reset those themselves if they wish to do that, instead of implicitly handling all of this when changing the rabbit type. However, the same is not possible yet for plugins in regards to the rabbit behavior.

Plugin code I used for testing this: https://pastebin.com/hDbKFvia