When you attach the click event you attach it to the existent elements in the DOM, when the ajax content comes, new DOM elements are created and the event wasn't attached to them.
One option is to use events delegation a way (but not recommended) to do it is using the document to read the event
$(document).on('click', 'button#submit', function(){
//do something
});
A better way is put the delegation to the element which gets the new content, lets assume is a form with an id formElement, It would be something like
$("#formElement").on('click', 'button#submit', function(){
//do something
});
Using that event delegation the new content from ajax will fire the click event.
PD if you have an ID in a element just use the id, like #submit, It makes a faster selector than tag#id because It used getElementById internaly