your JS should be wrapped to outputPanel and updated also on ajax requests which are updates the inputs and selects to which handlers is bound. in other case when DOM elements getting replaced with new ones from responce - them has no handlers attached anymore.
I think that this is exactly what is happening with me. On the other hand I am new to jquery, how can we do the update of the JS on the ajax request call so that handlers remains bound.
your JS should be wrapped to outputPanel and updated also on ajax requests
no, that issue about breaks about re-render. And in your case the reason of breaking - you not re-redering it. so add the panel as I suggested and check.