How do I view cookie or session information on the server?
More debug titbits.

Your question sounds like you're looking for the submitted/missing value name in the codebase - this form field name is probably not mentioned in the codebase if it's a value configured in the DB, as the form will then be generated.

Also, this name (say "volunteer_reason") may have been "munged" to a degree thanks to HTML_QuickForm's naming form inputs (you might see "contact_1_volunteer-reason_1" or whatever).

The most frequent cause of these not being populated as expected is when there is a mismatch between the originating and resulting request URLs. For those purposes, http://www.example.org and https://www.example.org are not the same thing; neither are http://example.org and http://www.example.org

This comment almost makes it sound like you're hitting session initialization issues - and that including the iframe prevents this. Weird.