Look at Element. Delegation to setup the event on the myDiv container one time, so you don't have to re-attach handlers each time the contents are updated. You need to include this MooTools-More extension in your scripts as it's not part of core yet, but will be starting from version 1.3.
You are attaching an event to an element that you are replacing. The dom has no way of knowing that to you, the old and the new button are identical. The old button is deleted (and the event listener with it) and the new button created.
So you need to re-attach the event to the new button.
When you set innerHTML on an element, the element's contents are completely cleared and replaced with a new set of elements -- the ones parsed from the innerHTML property. Any events set on the old elements will not apply to the new ones.
This is how JavaScript works, it's not a bug.
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