.on when used like that will only register once. You can register the event against an object you know will always be present.
You can give it some additional context such as a containing div so this may work better:
$('#div_test').on('click', '.f1_start', function(){
//.....
});
You could also register the current .on event you have inside the callback which would have the same effect and be slightly more efficient but in general doing things like that are better done through a proper revealing module pattern to only register events you require.
Also as another note, there is no need to empty the html and then set it, setting it will replace it.