I have a similar problem with a client.  Cannot reproduce it.  We have tried recording the user's session and as luck would have it the problem doesn't occur during our recording sessions!  They now export the sales orders lines to Excel.  After the order is picked they make sure the line count is the same.  If not, the Excel file is used to put the line back on the order.  It always seems to be the first line of the order that is missing but occasionally it is more.

Ours seems to be the last item entered on the invoice. We have locations in Oregon and Washington, and it appears that only our Washington invoices seem to drop items, so maybe it has something to do with the Taxable items?

Any there third-party integrations/enhancements in use? 

Are there extended descriptions on the item that is disappearing? ( see ) (Applies to an older version but worth considering)

There is also a recent report of odd line sorting but this appears to apply to invoices that are created from orders and there is no mention of disappearing lines ( see )

We do not have any third party integrations we are using. And we do not have extended descriptions, just extended Customer PO line. 

We have had a small amount of the Odd Line Sorting happening, but not very much, maybe once or twice a week, over 1200 invoices. 

I saw this with a client that was using Avatax a couple of years ago and I believe it was traced to a patch for Avatax,  however it looks like you are on the current version.

Same client is currently on 2016 and I recently had some people reporting dropped lines exactly as you are describing.   And of course we can't duplicate it on demand either.