The reason these fields are hidden is that when Forms saves a form submission, it opens the submission in the browser to capture the image. All of the JavaScript on your form will run when Forms does this, so if you have JavaScript that hides fields, those fields will be hidden. So, you need to do something to tell the JavaScript not to run.

If you only want to hide fields on the initial submission, you could wrap the JavaScript you're using to hide fields inside an IF statement, like this:

$(document).ready( function() {
if($('input[name="routingResumeId"]').val() =="") {
$("#ID").addClass('hidden'); //here's where you'd hide your fields, based on ID or class
}
});

Fields hidden this way will not be visible to the user filling them out, but will be visible in other tasks after the form has been submitted.

Another way to handle this is to make a copy of the form, remove the JavaScript that hides fields from the copy, and then use the copy in your Save to Repository service task.