I have never had this happen and obviously I cannot explain why this happening to you guys. I just tried to replicate this problem again on my own iPad and no matter what I sync from Pages or how I sync, I have no problems at all. I am not losing any files. Of course I am transferring the files back and forth using iOS file sharing which is what you supposed to do. The files will not sync to iTunes without using file sharing, but they should not be removed from the device either.
Here is the link again.
http://support.apple.com/kb/ht4094
You can try this. Launch iTunes on your computer, then select Preferences in iTunes from the drop down menu. I'm not sure where it is in the Windows version but Preferences is under the bold iTunes heading in the menu at the top. Then click on devices and look and see what the last date of your iPad's backup is. If it is the backup where you just lost your Pages app, the Pages files and data SHOULD be in the backup
You could connect your iPad to your computer and launch iTunes. Right click on your iPad's name on the left side under the devices heading and select backup. Then select the backup that was just created when you synced. Maybe that will restore the files to your iPad.
I wish I had another answer but that is the only thing I can come up with at this point. Maybe posting in the Pages for iPad area of the site would bring better results than I can offer. Here is the link to that site.
https://discussions.apple.com/community/app_store/iwork_for_ios