Shopify staff any updates on this? I've been following this thread closely as we have a handful of clients (some on plus, some on standard) that all have this issue. As it's been mentioned, it greatly skews the direct traffic conversion rate, while also misttributing sources in GA since that transaction gets attributed to Direct instead of the real source (ie. Paid Search, Organic, etc.) The sources in Shopify appear to be preserved, but not GA.
We've validated that it IS NOT the cart abandonment email since those numebers don't come close to adding up. This was validated across 5 seperate stores too.
The other reason for this that Shopify Plus Support mentioned is it could be the use of Buy Buttons or some app that truly does send someone straight to the /checkout/contact_information page. While I do believe this could be part of it for some, the stores that we validated this against don't utilize those functioanlities, so that removes that theory.
Basically that leaves what Joshua mentioned with someone taking longer than 2-minutes to checkout using a 3PPG then the linker (client-ID) ends up being dropped?
I'd like to mention that Better Reports has a number of reports built-in that show visits and sales by referring site (as well as utm source/campaign/medium).
This is relevant to this issue since the source is correctly preserved in Shopify, so these reports will show the correct traffic source.
Not for everyone, but for those who would consider using an app, this may be of help.
Aside from what I've shared, I suggest everyone look at their data following the checkout domain migration Shopify is rolling out to stores in July 2017. Having your own domain will clean up some issues created from cross-domain tracking, but I haven't confirmed yet how much it will.