I have a form that looks like this:
jQuery and Javascript on the client-side cannot persist to the server side. It has no access to write to code. You will have to gain access to a server-side language, or make use of some cloud-based services (you could, for example, persist to Amazon 3S, or a MongoDB or something of that nature, through Javascript API calls, on a cloud service).
While you could use Javascript/jQuery to construct an XML object in the client, you would then have to submit that to some server-side script to save it to a file.
Sorry to be the bearer of bad news, but you will need to get into something a bit more full-featured, if you want to be able to get this done.