I'm afraid that I'm not able to give you a definitive answer here. I'm not aware of any field referred to specifically as the "product ID". Unfortunately, seemingly standard data field names tend to vary from bank to bank. The documentation that Raynor mentioned appears to be specific documentation for one specific processor interface that we actually don't use.
Based on the wording that you quoted in the first post, it sounds like they are referring to a part of Interchange Compliance Data. This is a set of data used to tie an authorization to a capture if they are run separately. This is the only data "received at authorization" that is returned in the capture/settlement request. My best guess is that the "product ID" referenced by your bank refers to the Visa Transaction ID. They may call it something more generic like product ID because the actual name changes for each card type.
If my guess is correct (and without more detail it is a guess), then the most common cause of this data being missing is if you are mistakenly running "Authorize Only" transactions followed by "Capture Only". The correct followup transaction to an "Authorize Only" request is a "Prior Authorization Capture". As long as the correct transaction types are used, then Authorize.Net will automatically send back the Visa Transaction ID and similar fields.
