Yup, you attached what I wanted. So, I published your form to a library of mine, set the submit to submit to my library. I just tested it, and it works as anticipated. I open a new form from the library, I enter a few rows, enter data into all of them - submit and the data is in the XML and displayed when I re-open the form.
I do see that with your form you won't be overwriting existing XML and that you are using "now()" in the title, so you should be creating a new XML each time you submit. Maybe try deleting all the files in your test library and open from SharePoint again - that way when you submit there will be only one file in the library, in case of confusion....
I'm also wondering if maybe there is a problem with InfoPath Forms Services on your server, since the issue doesn't reproduce on my server - do you have a SharePoint Admin who could check the log files & see if anything is happening there?